Aspiration-based utility functions in a planning model for timber flow management.

The study presents a theory of utility models based on aspiration levels, as well as the application of this theory to the planning of timber flow economics. The first part of the study comprises a derivation of the utility-theoretic basis for the application of aspiration levels. Two basic models are dealt with: the additive and the multiplicative. Applied here solely for partial utility functions, aspiration and reservation levels are interpreted as defining piecewisely linear functions. The standpoint of the choices of the decision-maker is emphasized by the use of indifference curves. The second part of the study introduces a model for the management of timber flows. The model is based on the assumption that the decision-maker is willing to specify a shape of income flow which is different from that of the capital-theoretic optimum. The utility model comprises four aspiration-based compound utility functions. The theory and the flow model are tested numerically by computations covering three forest holdings. The results show that the additive model is sensitive even to slight changes in relative importances and aspiration levels. This applies particularly to nearly linear production possibility boundaries of monetary variables. The multiplicative model, on the other hand, is stable because it generates strictly convex indifference curves. Due to a higher marginal rate of substitution, the multiplicative model implies a stronger dependence on forest management than the additive function. For income trajectory optimization, a method utilizing an income trajectory index is more efficient than one based on the use of aspiration levels per management period. Smooth trajectories can be attained by squaring the deviations of the feasible trajectories from the desired one.

Bounded turning circles are weak-quasicircles

We show that a metric Jordan curve $\Gamma$ is \emph{bounded turning} if and only if there exists a \emph{weak-quasisymmetric} homeomorphism $\phi\colon \mathsf{S}^1 \to \Gamma$.

Metsäpirulainen : Liikemies Erik Johan Längman (1799-1863) talousjärjestelmän murroksessa

The Forest devil. Businessman Erik Johan Längman (1799 1863) in the transition of economic system In Finnish historiography, Erik Johan Längman (1799-1863) bears a bad reputation of his own level: a mean, profit-seeking businessman who did not care too much about methods in his operations. Although little known, Längman has been praised as one of the pioneers of modern industry in the Grand Duchy of Finland, which belonged to the Russian Empire. From the mid 1830s Längman owned iron mill and several sawmills around the country. The growing demand of the markets in the 1830s, especially in Great Britain, marked a strong stimulus to Finnish lumber industry. At the same time claims for stricter rule over the sawmill industry were raised by high officials. The momentum of the conflict, the Forest Act of 1851, brought an end to illegal overproduction. In this biography, particular emphasis is laid on the entrepreneurial behaviour of Längman, but also on the effect the entrepreneurs had on the Crown s policies. On the other hand, how did the limitations imposed by the Crown guide the actions of the sawmill owners? The solutions adopted by the sawmill owners and the manoeuvring of the government are in a constant dialogue in this study. The Finnish sawmill industry experienced a major change in its techniques and methods of acquiring timber during the 1830s. Längman particularly, with his acquisition organisation, was able to find and reach faraway forests with unexpected results. The official regulating system with its strict producing quotas couldn t follow the changes. When the battle against the sawmill industry really started on, in 1840, it didn t happen for the benefit of iron industry, as argued previously, but to save Crown forests from depletion. After the mid 1840s Längman and the leader of the Finnish nationalistic movement, J. V. Snellman questioned the rationality of the entire regulation system and in doing so they also posed a threat against the aristocratic power. The influential but now also badly provoked chairman of the economic division of senate, Lars Gabriel von Haartman, accused the sawmill-owners harder than ever and took the advantage of the reactionary spirit of imperial Russia to launch the state forest administration. Längman circumvented the conditions of privileges, felled Crown forests illegally and accusations were brought against him for destroying his competitors. The repeated conflicts spoke primarily about a superior business idea and organisational ability. Although Längman spent his last years mostly abroad he still had interests in Finnish timber business when the liberation of sawmill-industry was established, in 1861. Surprisingly, the antagonism around the Crown forests continued, probably even more heated.

Uskonto ilman uskontoa : Radikaalin postmodernin uskonnonfilosofian haaste

Religion without religion. The challenge of radical postmodern philosophy of religion. The aim of this study is to examine the central ideas of Mark C. Taylor, Don Cupitt, and Grace Jantzen on the subject of the philosophy of religion. The method is a qualitative, systematic analysis of the works of the aforementioned philosophers. The purpose is to present, analyze, identify, find connections, and to gain an understanding of the original texts. This thesis shows that radical postmodern religion is “religion without religion”. God is “dead” and the concept of God is seen as “writing”, an ideal, a relationship of meanings or a language. In ethics, there are no objective values or principles. People must create their own morality. Reality is each person´s concept of reality. Language is universal in that language and reality cannot be considered separately. The human subject is contingent and formed in the linguistic and social context. According to postmodern feminism, the ideas that men present as facts are often degrading to women, distort reality and support the power of men. For this reason, we should create a new kind of philosophy of religion and a new language that takes women into consideration. Finally, we will study some philosophers, who have used postmodern ideas in a more moderate manner. In this way, we will look for a balanced solution between modernism and postmodernism. This study shows that the postmodern idea of religion is very different from classical Christianity. Ethics becomes subjective, anarchistic and nihilistic. Epistemology is relativistic and the human being becomes the measure of all things. Objective reality becomes blurry. Language is seen to be game-like, and it has no relation to reality. The moral responsibility of a subject becomes problematic. Science and rationality come into question without the permanent core provided by our consciousness. Women are not in an epistemologically privileged position. The truth claims by either men or women must each be evaluated one at a time. Many postmodern ideas can successfully be made of use if used in moderate manner.

Leibniz on Rational Decision-Making

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality.

Scheffleriläinen rationaalisuus ja kasvatustodellisuuden monikerroksisuus : Jännitteitä ja ratkaisuja Israel Schefflerin kasvatusfilosofiassa

The study is a philosophical analysis of Israel Scheffler’s philosophy of education, focusing on three crucial conceptions in his philosophy: the conception of rationality, the conception of human nature, and the conception of reality. The interrelations of these three concepts as well as their relations to educational theorizing are analysed and elaborated. A conceptual problem concerning Scheffler’s ideal of rationality derives from Scheffler’s supposition of the strong analogy between science education and moral education in terms of the ideal of rationality. This analogy is argued to be conceptually problematic, since the interconnections of rationality, objectivity, and truth, appear to differ from each other in the realms of ethics and science, given the presuppositions of ontological realism and ethical naturalism, to which Scheffler explicitly subscribes. This study considers two philosophical alternatives for solving this problem. The first alternative relates the analogy to the normative concept of personhood deriving from the teleological understanding of human nature. Nevertheless, this position turns out to be problematic for Scheffler, since he rejects all teleological thinking in his philosophy. The problem can be solved, as it is argued, by limiting Scheffler’s rejection of teleology – in light of his philosophical outlook on the whole – in a manner that allows a modest version of a teleological conception of human nature. The second alternative, based especially on Scheffler’s later contributions, is to suggest that reality is actually more complex and manifold than it appears to be in light of a contemporary naturalist worldview. This idea of plurealism – Scheffler’s synthesis of pluralism and realism – is represented especially in Scheffler’s contributions related to his debate with Nelson Goodman dealing with both constructivism and realism. The idea of plurealism is not only related to the ethics-science-distinction, but is more widely related to the relationship between ontological realism and the incommensurable systems of description in diverse realms of human understanding. The Scheffler-Goodman debate is also analysed in relation to the contemporary constructivism-realism debate in educational philosophy. In terms of educational questions, Scheffler’s plurealism is argued as offering a fruitful perspective. Scheffler’s philosophy of education can be interpreted as searching for solutions to the problems deriving from the tension between the tradition of analytical philosophy and the complexity and multiplicity of educational reality. The complexity of reality combined with the supposition of the limitedness of human knowledge does not lead Scheffler to relativism or particularism, but, in contrast, Schefflerian formulations of rationality and objectivity preserve the possibility for critical inquiry in all realms of educational reality. In light of this study, Scheffler’s philosophy of education provides an exceptional example of combining ontological realism, epistemological fallibilism, and the defence of the ideal of rationality, combined with a wide-ranging understanding of educational reality.

Visual completion in an illusory figure

The visual systems of humans and animals represent physical reality in a modified way, depending on the specific demands that the species in question has for survival. The ability to perceive visual illusions is found in independently evolved visual systems, from honeybees to humans. In humans, the ability emerges early, at the age of four months. Thus the perception of illusion is likely to reflect visual processes of fundamental importance for object perception in natural vision. The experiments reported in this thesis employed various modifications of the Kanizsa triangle, a drawn configuration composed of three black disks with missing sectors on a white background. The sectors appear to form the tips of a triangle. The visual system completes the physically empty area between the disks, generally called inducers, with giving the perception of an illusory triangle. The illusory triangle consists of an illusory surface bounded by illusory contours; the triangle appears brighter than and to lie above the background. If the sectors are coloured, the colour fills the illusory area, a phenomenon known as neon colour spreading . We investigated spatial limitations on the perception of Kanizsa-type illusions and how other stimuli and viewing parameters affected these limitations. We also studied complex configurations thick, bent, mobile and chromatic inducers - to determine whether illusions combining several attributes can be perceived. The results suggest that the visual system is highly effective in completing a percept. The perception of an illusory figure is spatially scale invariant when perceived at threshold. The processing time and the number of fixations modify the percept, making the perception of the illusion more probable in various viewing conditions. Furthermore, the fact that the illusion can be perceived when only one inducer is physically present at any given moment indicates the potential of single inducers. Apparently, modelling illusory figure perception will require a combination of low-level, local processes and higher-level integrative processes. Our studies with stimuli combining several attributes relevant to object perception demonstrate that the perception of an illusory figure is flexible and is maintained also when it contains colour and volume and when shown in movement. All in all, the results confirm the assumed importance of the visual processes related with the perception of illusory figures in everyday viewing. This is indicated by the variety of inducer modifications that can be made without destroying the percept. Furthermore, the illusion can acquire additional attributes from such modifications. Due to individual differences in the perception of illusory figures, universal values for absolute performance are not always meaningful, but stable trends and general relations do exist.

Koulukasvatusta teknologisoituvaan yhteiskuntaan : Kansakoulun opetussuunnitelman rakentuminen, 1945-1952

Education for a Technological Society. Public School Curriculum Construction, 1945-1952. The subject of my research is the significance of technology in the construction process of the public school curriculum during the years 1945-1952. During the period the war reparation and rebuilding placed demands and actions to rationalise and dramatise industry and agriculture. Thereby the ambitions of building a technological country and the reformation of curriculum took place simultaneously. Fordistian terms of reference, of which the principles were mass production, rationalisation and standardisation, a hierarchical division of labour and partition of assignments, provided a model for the developing curriculum. In the research the curriculum is examined as an artefact, which shapes socio-technically under the influence of social and technical factors. In the perspective of socio-technical construction the artefact is represented by the viewpoints of members of relevant social groups. The groups give meaning to the curriculum artefact, which determines the components of the curriculum. The weakness of the curriculum was its ineffectiveness, which was due to three critical problems. Firstly, the curriculum was to be based on scientific work, which meant the development of schools through experiments and scientific research. Secondly, the civilised conseption in the curriculum was to be composed of theoretical knowledge, as well as practical skills. Practical education was useful for both the individual and society. Thirdly, the curriculum was to be reformed in a way that the individuality of the pupil would be taken into account. It was useful for the society that talents and natural abilities of every pupil were observed and used to direct the pupil to the proper place in the social division of labour, according to the "right man in a right place" principle. The solutions to critical problems formed the instructions of the public school curriculum, which described the nature and content of education. Technology and its development were on essential part of the whole school curriculum process. The quality words connected to the development of technology - progress, rationality and effectiveness - were also suitable qualifiers and reasons for the reform of the curriculum. On the other hand, technology set a point of comparison and demand for the development of all phases of education. The view of technology was not clearly deterministic - it was also possible to shape technological society with the help of education. The public school curriculum process indicates how originally the principles of technological systems were shaped to the language of education and accepted in educational content.

Arjen hallinta kotitalouden toiminnan tavoitteena : Kotitalouden toiminnan filosofista ja teoreettista tarkastalua

The aim of this philosophical and theoretical study is to outline a conceptual framework, which could be used to describe the qualitative characteristics of household activities from a holistic point of view. The philosophical part of the study deals with ontological and epistemological approaches. Ontological questions of existence are based on the holistic notion of man. The epistemological approach to household activities is based on the Aristotelian concept of knowledge, according to which actions are viewed as being praxis and poiesis in type. The concept of rationality is essential. As a result of the study, concepts describing the qualitative contents of the concept of mastery of everyday life are presented. Mastery of everyday life describes an individual's understanding of how to act in a household and promote the common good. The qualitative dimensions are the aims of actions, knowledge that guides actions and interaction. From the standpoint of these dimensions, the development of mastery of everyday life means an increase in the individual's sense of responsibility, so that s/he is gradually able to deal responsibility with the whole household, the immediate environment and the surrounding community and society. The quality of interaction develops so that the significance of communicative interaction becomes central. There are three levels in the mastery of everyday life, which differ from one other in respect to the development of reflective thought and the scope of understanding. The whole conceptual framework will contribute to the study of both household activities and the teaching of home economics. Key words: holistic notion of man, rationality, interaction.

Yhteinen käsityö peruskoulun 7. luokalla : Opettajien kokemuksia yhteisen käsityön opetuksesta ja organisoinnista

Finnish education politics presume that basic education should be equal to all students. While organising craft education equality can be understood as similarity or as possibility to choose. The possibility to be able to choose whether textile or technical craft despite of one´s gender has been the aim of laws and curriculums already over 30 years. In practice it´s almost impossible to students to ignore feminine and masculine roles that go deep into our culture. Choosing craft has been divided by gender, which is the reason why possibility to choose has not been good enough to educationalists of equality. The latest guidelines for the National core curriculum for bacis education were issued in 2004. According to curriculum craft education consists parts of both technical and textile craft. All students should take part in both sectors of crafts. Furthermore, one can be given a possibility to consentrate his studies in whether textile or technical craft. The curriculum does not set the rules how the education should be organised, which means that it can be organised in many ways depending on city, school or teacher. Teachers and other specialists have contradictory feelings towards shared craft education, because traditional way to see craft in Finland is to separate textile craft from technical craft. Both crafts have some common features that are introduced in curriculum. Besides there is many equal things in craft theories that bind textile and technical craft to each other. The main purpose of this research was to find out, how shared craft education has been organised at the 7.th grade in Finnish comprehensive school, and which things affect in the settlements. Second goal was to describe and compare teachers´ experiences in teaching shared craft education. Third aim of this study was how shared craft has changed craft education. I collected the research material in May 2006 by interviewing both textile and technical craft teachers who teach shared craft. The material consists of fourteen theme interviews. In the analysis of the material I used theoretic bounded document analysis. According to the research there are three different ways to organise shared craft education: 50 50-arrangement, exchanging period and project week. In the schools that carried out 50 50-arrangement teaching was realised mainly in heterogenous groups. Principals had usual a lot of authorization on how to arrange craft education, which means that their views on equality, laws and curriculum affected in the settlemets more than teachers´ opinions. Teachers´ attitudes to shared craft were mainly positive. The changing of craft education can be divided in two parts: the aims and the containings of the curriculum have changed, as well as the meaning of the craft as core subject. Teachers have been forced to decrease the containings of both textile and technical crafts. Despite of eliminations both crafts still have comprehensive containings. Teachers decided what to teach by these argumets: Students should learn some basic things or produce a certain product. Usually teachers had also a lot of experience and special intrests in crafts. According to this research there is four significant meanings for shared craft education: 1) developing readiness for doing things, 2) developing skills of thinking, 3) delight of doing things and 4) teaching attitude.

Concentrate feeding strategies for growing and finishing dairy bulls offered grass silage-based diets

The first aim of this thesis was to produce data for evaluating, developing and recommending biologically and economically efficient energy and protein feeding strategies for growing and finishing dairy bulls offered grass silage-based diets. The second aim was to calculate the energy and protein supplies of the dairy bulls fed different grass silage-cereal-based diets and, based on this, to estimate the possible need to revise the current Finnish energy and protein recommendations for growing dairy bulls. The third aim was to demonstrate the phosphorus supply of dairy bulls fed grass silage-cereal-based diets with or without protein supplementation in relation to current feeding recommendations for phosphorus. The results indicate that protein supplement is not needed for finishing dairy bulls (live weight more than 250 kg) when they are fed good-quality grass silage (digestible organic matter more than 650 g/kg dry matter, restricted fermentation with low concentrations of fermentation acids and ammonia N) and grain-based concentrate with a moderate (300-700 g/kg dry matter) concentrate level. The results also suggest that with total mixed ration feeding it is possible to use rather high concentrate proportions (700 g/kg dry matter) in feeding dairy bulls. According to this study, barley fibre is a suitable energy supplement with good-quality silage for growing dairy bulls. The results suggest that 50% of barley grain can be replaced with barley fibre without affecting growth. Also oats is a suitable energy supplement for dairy bulls. However, as a consequence of decreased energy intake, the gain and feed conversion of the bulls were slightly reduced in this study when barley grain was replaced by oats in the diet. Ultimately, the rationality of the use of barley fibre and oats in the future will depend on the price in relation to other concentrates. During the feeding experiments the calculated supply of energy was 10% higher than in the Finnish feeding recommendations for the present growth rate. This indicates that there is a need to update the Finnish feeding recommendations for dairy-breed growing bulls, and further calculations are needed for the energy supply of growing dairy bulls. The calculated supply of AAT (amino acids absorbed from the small intestine) was 38% higher than in the Finnish feeding recommendations for the present growth. Possibly, the present AAT-PBV system is not an optimal protein evaluation system for growing dairy bulls more than 250 kg live weight. The calculations based on the feeding experiments and the Finnish feeding recommendations indicate that in most cases the dairy bulls (live weight more than 250 kg) received enough P from the basic grass silage cereal-based diets without additional mineral feeds. Therefore there is no need to add P in the form of mineral mixtures.

Tietämisen politiikka : Kokemuksellinen tieto kunnan hallinnassa

The present study examines citizen participation in local government and municipal democracy. Previous research has shown that the prerequisite for active citizenship lies in the opportunities available for local residents to determine which perspectives and planning needs are relevant. This research looks at whether the conception of knowledge employed in municipal planning allows for this kind of active role for local citizens. Methodologically the study employs an hermeneutic approach. The aim has been to identify various approaches steering the practice of municipal democracy. The theory behind the study comes from the assumption of the intersubjectivity of reality. Construing the rationality of one s own behaviour is seen as a prerequisite for meaningful action. In this context, criteria for the functionality of municipal democracy and the purpose of strengthening citizen participation are defined. The study is divided into two parts. Firstly, the purpose of participation and the opportunities for local residents to contribute is examined theoretically with reference to previous studies. The intention is to provide an overview of the Finnish cross-disciplinary debate on resident participation. This debate is reflected onto the prevailing views on changes in the municipal operating environment and modes of operation. In conclusion, a theoretical model is constructed to explain how the various modes of operation in regional municipalities affect the purpose of resident participation and the utilisation of information received through this participation. The second part of the study discusses the utilisation of this information and knowledge acquired through the participation of local residents and all those involved in political and administrative processes in municipalities. These first-hand reports are analysed using the model constructed earlier in the study. The goal is to understand how political and administrative practice affects opportunities for local residents to participate and contribute. The core of this analysis is based on the pragmatic conception of knowledge employed in municipal administration. The study argues that the normal practice of municipal administration does not support the systematic utilisation of local residents experience. This is caused by two interlinked factors: firstly, knowledge constructed through these practices requires that the knowledge is apolitical; secondly, arising from this there is confusion with regard to when during a planning process does information obtained from the public become relevant; in other words, what are the politics of knowledge? The study suggests that the solution is in the complementary concept of knowledge, which implicitly acknowledges the politics of knowledge. The complementary concept of knowledge would serve the politicisation of issues on the level of interpretations linked with social reality, an indispensable requirement for functional democracy. Keywords: participation, municipal democracy, knowledge base for planning, experiential knowledge

Aluesuunnittelu ja kestävä kehitys Luoteis-Venäjällä : Ympäristösuunnittelun mahdollisuus paikallisissa hallintatavoissa

In this Ph.D. thesis I have studied how the objectives of sustainable development have been integrated into Northwest Russian urban and regional planning, and how the Russian planning discourse has changed after the collapse of the Soviet Union. By analysing the planning discussion, processes, and strategic documents I have also investigated the use of power and governmentality in urban and regional planning. As a methodological foundation I have used an approach that I call geographical constructivism . It was possible to answer in a relevant manner the question of how sustainable development has become a part of planning in Northwest Russia through a discourse analysis of the planning discussion. During the last decades, the aim of sustainable development has become globally one of the most central societal challenges. Urban and regional planning has a central role to play in promoting this process, since many meta-level objectives actually take shape within its sphere. An ever more actual challenge brought by sustainable development is to plan regions and places while balancing the conflicts of the pressures of safeguarding a good environment and of taking into consideration social and economic needs. I have given these unavoidable conflicts of sustainable development a central place in my work. In my view, complementing instrumental and communicative rationality with conflict rationality gives environmental planning a well-equipped toolbox. Sustainable development can be enhanced in urban and regional planning by seeking open, and especially hidden, potential conflicts. Thus, the expressed thinking (mentality) and actions taken by power regimes in and around conflicts open an interesting viewpoint into Northwest Russian governmentality. I examine the significance of sustainable development in planning through Northwest Russian geography, and also through recent planning legislation and four case studies. In addition, I project my analysis of empirical material onto the latest discussion of planning theory. My four case studies, which are based on independent and separate empirical material (42 thematic interviews and planning documents), consider the republics of Karelia and Komi, Leningrad oblast and the city of Saint Petersburg. In the dissertation I argue how sustainable development is, in the local governmentalities of Northwest Russia, understood as a concept where solving environmental problems is central, and that they can be solved through planning carried out by the planning professionals. Despite this idealism, environmental improvements have been overlooked by appealing to difficult economic factors. This is what I consider environmental racism, which I think is the most central barrier to sustainable development in Northwest Russia. The situation concerning the social dimension of sustainable development is even more difficult, since, for example, the development of local democracy is not highly valued. In the planning discourse this democracy racism is explained by a short history of democracy in Russia. However, precisely through planning conflicts, for example in St. Petersburg, planning has become socially more sustainable: protests by local inhabitants have bypassed the poorly functioning representational democracy, when the governmentality has changed from a mute use of power to one that adopts a stand on a conflicting issue. Keywords: Russia, urban and regional planning, sustainable development, environmental planning, power and conflicts in planning, governmentality, rationalities.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.