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.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Essays on the Economics of Intellectual Property Rights

Väitöskirjassani tarkastelen informaatiohyödykkeiden ja tekijänoikeuksien taloustiedettä kahdesta eri perspektiivistä. Niistä ensimmäinen kuuluu endogeenisen kasvuteorian alaan. Väitöskirjassani yleistän ”pool of knowledge” -tyyppisen endogeenisen kasvumallin tilanteeseen, jossa patentoitavissa olevalla innovaatiolla on minimikoko, ja jossa uudenlaisen tuotteen patentoinut yritys voi menettää monopolinsa tuotteeseen jäljittelyn johdosta. Mallin kontekstissa voidaan analysoida jäljittelyn ja innovaatioilta vaaditun ”minimikoon” vaikutuksia hyvinvointiin ja talouskasvuun. Kasvun maksimoiva imitaation määrä on mallissa aina nolla, mutta hyvinvoinnin maksimoiva imitaation määrä voi olla positiivinen. Talouskasvun ja hyvinvoinnin maksimoivalla patentoitavissa olevan innovaation ”minimikoolla” voi olla mikä tahansa teoreettista maksimia pienempi arvo. Väitöskirjani kahdessa jälkimmäisessä pääluvussa tarkastelen informaatiohyödykkeiden kaupallista piratismia mikrotaloustieteellisen mallin avulla. Informaatiohyödykkeistä laittomasti tehtyjen kopioiden tuotantokustannukset ovat pienet, ja miltei olemattomat silloin kun niitä levitetään esimerkiksi Internetissä. Koska piraattikopioilla on monta eri tuottajaa, niiden hinnan voitaisiin mikrotaloustieteen teorian perusteella olettaa laskevan melkein nollaan, ja jos näin kävisi, kaupallinen piratismi olisi mahdotonta. Mallissani selitän kaupallisen piratismin olemassaolon olettamalla, että piratismista saatavan rangaistuksen uhka riippuu siitä, kuinka monille kuluttajille piraatti tarjoaa laittomia hyödykkeitä, ja että se siksi vaikuttaa piraattikopioiden markkinoihin mainonnan kustannuksen tavoin. Kaupallisten piraattien kiinteiden kustannusten lisääminen on mallissani aina tekijänoikeuksien haltijan etujen mukaista, mutta ”mainonnan kustannuksen” lisääminen ei välttämättä ole, vaan se saattaa myös alentaa laillisten kopioiden myynnistä saatavia voittoja. Tämä tulos poikkeaa vastaavista aiemmista tuloksista sikäli, että se pätee vaikka tarkasteltuihin informaatiohyödykkeisiin ei liittyisi verkkovaikutuksia. Aiemmin ei-kaupallisen piratismin malleista on usein johdettu tulos, jonka mukaan informaatiohyödykkeen laittomat kopiot voivat kasvattaa laillisten kopioiden myynnistä saatavia voittoja jos laillisten kopioiden arvo niiden käyttäjille riippuu siitä, kuinka monet muut kuluttajat käyttävät samanlaista hyödykettä ja jos piraattikopioiden saatavuus lisää riittävästi laillisten kopioiden arvoa. Väitöskirjan viimeisessä pääluvussa yleistän mallini verkkotoimialoille, ja tutkin yleistämäni mallin avulla sitä, missä tapauksissa vastaava tulos pätee myös kaupalliseen piratismiin.

Studies on the Effects of Property Taxation, Rent Control and Housing Allowances

Tämä väitöskirja koostuu asuntomarkkinoiden taloustieteellistä analyysia esittelevästä johdantoluvusta ja kolmesta tutkimuksesta, joissa analysoidaan asuntomarkkinoihin vaikuttavia politiikkatoimenpiteitä. Luvussa 2 tutkitaan Suomen kiinteistöverojärjestelmän vaikutusta asuntorakentamiseen. Vuonna 2001 tehtiin uudistus, jonka myötä kunnat voivat verottaa rakentamatonta asuintonttia korkeammalla veroasteella kuin rakennettua tonttia. Maanomistajan rakentamispäätöksen teoreettisen mallin mukaan rakentamattoman tontin korotettu kiinteistöveron pitäisi nopeuttaa rakentamista, mutta toisaalta myös rakentamiseen investoitu rahamäärä saattaa muuttua. Asuintonttien kiinteistöverojen yleinen taso ei vaikuta maanomistajan käyttäytymiseen, sillä tontin verotusarvo ei riipu rakentamispäätöksestä. Vain rakentamattoman ja rakennetun tontin veroasteiden erolla on merkitystä. Empiiriset tulokset ovat sopusoinnussa teorian kanssa. Tulosten mukaan prosenttiyksikön nousu rakentamattoman ja rakennetun tontin veroasteiden erossa lisää omakotialoitusten määrää viidellä prosentilla lyhyellä aikavälillä. Luvussa 3 analysoidaan vuokrasääntelystä vuokralaisille aiheutuvia hyötyjä ja haittoja. Vuokrasäännellyissä asunnoissa asuvat kotitaloudet hyötyvät vuokrasääntelystä alhaisen vuokran muodossa. Heille saattaa kuitenkin koitua myös haittaa siitä, että toiveita vastaavan asunnon löytäminen on vuokrasääntelytilanteessa vaikeaa, koska vapaille asunnoille on suuri määrä ottajia. Vapaarahoitteisen vuokra-asuntokannan vuokrien sääntely purettiin Suomessa asteittain vuosina 1992–1995. Tutkimuksen empiiriset tulokset viittaavat siihen, että vuokrasääntelyn aiheuttamista suurista eroista halutun ja todellisen asuntokulutuksen välillä koituvat hyvinvointitappiot kumosivat merkittävän osan matalien vuokrien hyödyistä vuokralaisille. Luvussa 4 tutkitaan Suomen asumistukijärjestelmän kannustinvaikutuksia. Asumistuen määrää rajoittavat asunnon pinta-alalle ja neliövuokralle asetetut ylärajat. Neliövuokrarajoite voidaan tulkita asumisen laatua rajoittavana tekijänä. Tutkimuksen teoreettisessa osassa osoitetaan, että asumistukijärjestelmä luo vahvat kannustimet muuttaa asuntoihin, joissa pinta-ala- ja laaturajoitteet purevat. Empiiristen tulosten mukaan asumistukeen oikeutetut kotitaloudet eivät näytä reagoivan kannusteisiin. Tukeen oikeutettujen kotitalouksien asumisvalinnat suhteessa pinta-ala ja laaturajoitteisiin vastaavat muiden kotitalouksien valintoja ja asunnonvaihdon mahdollistama potentiaalinen asumistuen lisäys ei nosta muuttotodennäköisyyttä. Muuttamiseen liittyvät kustannukset ja vajavaiset tiedot tukijärjestelmästä saattavat selittää heikkoa reagointia asumistuen luomiin kannustimiin. Toinen mahdollinen selitys on asumistuen vajaakäyttö. Tutkimuksen mukaan vain 70–80 prosenttia asumistukeen oikeutetuista kotitalouksista nostaa tukea. Asumistuen hyödyntämisen todennäköisyys riippuu koulutustasosta, tuen määrästä ja tulo-odotuksista.

Modelling and Forecasting Property Rents and Returns (summary section only)

Recently, focus of real estate investment has expanded from the building-specific level to the aggregate portfolio level. The portfolio perspective requires investment analysis for real estate which is comparable with that of other asset classes, such as stocks and bonds. Thus, despite its distinctive features, such as heterogeneity, high unit value, illiquidity and the use of valuations to measure performance, real estate should not be considered in isolation. This means that techniques which are widely used for other assets classes can also be applied to real estate. An important part of investment strategies which support decisions on multi-asset portfolios is identifying the fundamentals of movements in property rents and returns, and predicting them on the basis of these fundamentals. The main objective of this thesis is to find the key drivers and the best methods for modelling and forecasting property rents and returns in markets which have experienced structural changes. The Finnish property market, which is a small European market with structural changes and limited property data, is used as a case study. The findings in the thesis show that is it possible to use modern econometric tools for modelling and forecasting property markets. The thesis consists of an introduction part and four essays. Essays 1 and 3 model Helsinki office rents and returns, and assess the suitability of alternative techniques for forecasting these series. Simple time series techniques are able to account for structural changes in the way markets operate, and thus provide the best forecasting tool. Theory-based econometric models, in particular error correction models, which are constrained by long-run information, are better for explaining past movements in rents and returns than for predicting their future movements. Essay 2 proceeds by examining the key drivers of rent movements for several property types in a number of Finnish property markets. The essay shows that commercial rents in local markets can be modelled using national macroeconomic variables and a panel approach. Finally, Essay 4 investigates whether forecasting models can be improved by accounting for asymmetric responses of office returns to the business cycle. The essay finds that the forecast performance of time series models can be improved by introducing asymmetries, and the improvement is sufficient to justify the extra computational time and effort associated with the application of these techniques.

The North in the Old English Orosius : A Geographical Narrative in Context

This doctoral dissertation examines the description of the North as it appears in the Old English Orosius (OE Or.) in the form of the travel accounts by Ohthere and Wulfstan and a catalogue of peoples of Germania. The description is discussed in the context of ancient and early medieval textual and cartographic descriptions of the North, with a special emphasis on Anglo-Saxon sources and the intellectual context of the reign of King Alfred (871-899). This is the first time that these sources, a multidisciplinary approach and secondary literature, also from Scandinavia and Finland, have been brought together. The discussion is source-based, and archaeological theories and geographical ideas are used to support the primary evidence. This study belongs to the disciplines of early medieval literature and (cultural) history, Anglo-Saxon studies, English philology, and historical geography. The OE Or. was probably part of Alfred s educational campaign, which conveyed royal ideology to the contemporary elite. The accounts and catalogue are original interpolations which represent a unique historical source for the Viking Age. They contain unparalleled information about peoples and places in Fennoscandia and the southern Baltic and sailing voyages to the White Sea, the Danish lands, and the Lower Vistula. The historical-philological analysis reveals an emphasis on wealth and property, rank, luxury goods, settlement patterns, and territorial divisions. Trade is strongly implied by the mentions of central places and northern products, such as walrus ivory. The references to such peoples as the Finnas, the Cwenas, and the Beormas appear in connection with information about geography and subsistence in the far North. Many of the topics in the accounts relate to Anglo-Saxon aristocratic culture and interests. The accounts focus on the areas associated with the Northmen, the Danes and the Este. These areas resonated in the Anglo-Saxon geographical imagination: they were curious about the northern margin of the world, their own continental ancestry and the geography of their homeland of Angeln, and they had an interest in the Goths and their connection with the southern Baltic in mythogeography. The non-judgemental representation of the North as generally peaceful and relatively normal place is related to Alfredian and Orosian ideas about the unity and spreading of Christendom, and to desires for unity among the Germani and for peace with the Vikings, who were settling in England. These intellectual contexts reflect the innovative and organizational forces of Alfred s reign. The description of the North in the OE Or. can be located in the context of the Anglo-Saxon worldview and geographical mindset. It mirrors the geographical curiosity expressed in other Anglo-Saxon sources, such as the poem Widsith and the Anglo-Saxon mappa mundi. The northern section of this early eleventh-century world map is analyzed in detail here for the first time. It is suggested that the section depicts the North Atlantic and the Scandinavian Peninsula. The survey of ancient and early medieval sources provides a comparative context for the OE Or. In this material, produced by such authors as Strabo, Pliny, Tacitus, Jordanes, and Rimbert, the significance of the North was related to the search for and definition of the northern edge of the world, universal accounts of the world, the northern homeland in the origin stories of the gentes, and Carolingian expansion and missionary activity. These frameworks were transmitted to Anglo-Saxon literary culture, where the North occurs in the context of the definition of Britain s place in the world.

Kuluttaminen ja ylhäisaatelin elämäntapa 1700-luvun Ruotsissa

Consumption and the lifestyle of the high nobility in eighteenth-century Sweden This monograph is an analysis of the lifestyle, consumption and private finances of the Swedish high nobility during the eighteenth century (ca 1730 1795). It describes the lifestyle of one noble house, the House of Fersen. The Fersen family represents the leading political, economic and cultural elite in eighteenth-century Sweden. The analysis concentrates on Count Carl von Fersen (1716 1786) and his brother Count Axel von Fersen (1719 1794), their spouses and children. Carl von Fersen was a courtier whilst Axel von Fersen was an officer and one of the leaders of the Francophile Hat party. His son, Axel von Fersen the younger, was in his time an officer and a favourite of Gustavus III, King of Sweden, as well as a favourite and trusted confidant of Marie-Antoinette, Queen of France. The research is based upon the Fersen family s private archives, the Counts personal account books, probate inventories, letters and diaries. The study discusses the Fersens landed property and investments in ironworks and manufacturing, the indebtedness of the high nobility, high offices in civil administration, the militia and at court, as well as marriages as the foundations of noble wealth and power. It analyses the Count von Fersens revenue and expenditure, their career options and personal expenses, their involvement in the building and decorating of palaces, and the servants in service of the Fersen family as well as the ideal nobleman and his consumption. Central themes are inheritance, children s education, marriages and ladies preparing their trousseaux, the nobility ordering luxury goods from France, the consumption of Counts and Countesses before and after marrying and having children, the pleasures of a noble life as well as the criticism of luxury and sumptuousness. The study contributes to the large body of research on consumption and nobility in the eighteenth century by connecting the lifestyle, consumption and private finances of the Swedish high nobility to their European context. Key words: nobility, Fersen, lifestyle, consumption, private finances, Sweden, eighteenth century

"Secoituxesta järjettömäin luondocappalden canssa" : Perversiot, oikeuselämä ja kansankulttuuri 1700-luvun Suomessa

Bestiality was in the 18th century a more difficult problem in terms of criminal policy in Sweden and Finland than in any other Christian country in any other period. In the legal history of deviant sexuality, the phenomenon was uniquely widespread by international comparison. The number of court cases per capita in Finland was even higher than in Sweden. The authorities classified bestiality among the most serious crimes and a deadly sin. The Court of Appeal in Turku opted for an independent line and was clearly more lenient than Swedish courts of justice. Death sentences on grounds of bestiality ended in the 1730s, decades earlier than in Sweden. The sources for the present dissertation include judgment books and Court of Appeal decisions in 253 cases, which show that the persecution of those engaging in bestial acts in 18th century Finland was not organised by the centralised power of Stockholm. There is little evidence of local campaigns that would have been led by authorities. The church in its orthodoxy was losing ground and the clergy governed their parishes with more pragmatism than the Old Testament sanctioned. When exposing bestiality, the legal system was compelled to rely on the initiative of the public. In cases of illicit intercourse or adultery the authorities were even more dependent on the activeness of the local community. Bestiality left no tangible evidence, illegitimate children, to betray the crime to the clergy or secular authorities. The moral views of the church and the local community were not on a collision course. It was a common view that bestiality was a heinous act. Yet nowhere near all crimes came to the authorities' knowledge. Because of the heavy burden of proof, the legal position of the informer was difficult. Passiveness in reporting the crime was partly because most Finns felt it was not their place to intervene in their neighbours' private lives, as long as that privacy posed no serious threat to the neighbourhood. Hidden crime was at least as common as crime more easily exposed and proven. A typical Finnish perpetrator of bestiality was a young unmarried man with no criminal background or mental illness. The suspects were not members of ethnic minorities or marginal social groups. In trials, farmhands were more likely to be sentenced than their masters, but a more salient common denominator than social and economical status was the suspects' young age. For most of the defendants bestiality was a deep-rooted habit, which had been adopted in early youth. This form of subculture spread among the youth, and the most susceptible to experiment with the act were shepherds. The difference between man and animal was not clear-cut or self-evident. The difficulty in drawing the line is evident both in legal sources and Finnish folklore. The law that required that the animal partners be slaughtered led to the killing of thousands of cows and mares, and thereby to substantial material losses to their owners. Regarding bestiality as a crime against property motivated people to report it. The belief that the act would produce human-animal mongrels or that it would poison the milk and the meat horrified the public more than the teachings of the church ever could. Among the most significant aspects in the problems regarding the animals is how profoundly different the worldview of 18th century people was from that of today.