Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Aineellista ja aineetonta turvaa : Ruokakunnat, ekologis-taloudelliset resurssit ja kontaktinmuodostus Valkealassa 1630 1750

Material and immaterial security. Households, ecological and economic resources and formation of contacts in Valkeala parish from the 1630s to the 1750s. The geographical area of the thesis, Valkeala parish in the region of Kymenlaakso, is a very interesting area owing to its diversity, both in terms of natural setting and economic and cultural structure. The study begins by outlining the ecological and economic features of Valkeala and by analysing household structures. The main focus of the research lies in the contacts of the households with the outside world. The following types of contacts are chosen as indicators of the interaction: trade and credit relations, guarantees, co-operation, marriages and godparentage. The main theme of the contact analysis is to observe the significance of three factors, namely geographical extent, affluence level and kinship, to the formation of contacts. It is also essential to chart the interdependencies between ecological and economic resources, changes in the structure of households and the formation of contacts during the period studied. The time between the 1630s and the 1750s was characterized by wars, crop losses and population changes, which had an effect on the economic framework and on the structural variation of households and contact fields. In the 17th and 18th centuries Valkeala could be divided, economically, into two sections according to the predominant cultivation technique. The western area formed the field area and the eastern and northern villages the swidden area. Multiple family households were dominant in the latter part of the 17th century, and for most of the study period, the majority of people lived in the more complex households rather than in simple families. Economic resources had only a moderate impact on the structure of contacts. There was a clear connection between bigger household size and the extent and intensity of contacts. The jurisdictional boundary that ran across Valkeala from the northwest to the southeast and divided the parish into two areas influenced the formation of contacts more than the parish boundaries. Support and security were offered largely by the primary contacts with one s immediate family, neighbours and friends. Economic support was channelled from the wealthier to the less well off by credits. Cross-marriages, cross-godparentage and marital networks could be seen as manifestations of an aim towards stability and the joining of resources. It was essential for households both to secure the workforce needed for a minimum level of subsistence and to ensure the continuation of the family line. These goals could best be reached by complex households that could adapt to the prevailing circumstances and also had wider and more multi-layered contacts offering material and immaterial security.

Non-finite constructions in Old English : with special reference to syntactic borrowing from Latin

My dissertation is a corpus-based study of non-finite constructions in Old English (OE). It revisits the question of Latin influence on the OE syntax, offering a new evaluation of syntactic interference between Latin and OE, and, more generally, of the contact situation in the OE period, drawing on methods used in studying grammaticalization and language contact. I address three non-finite constructions: absolute participial construction, accusative-and-infinitive construction, and nominative-and-infinitive construction, exemplified respectively in present-day English as - She looked like a pixie sometimes, her eyes darting here and there, forever watchful (BNC CCM 98); - My first acquaintance with her was when I heard her sing (BNC CFY 2215); - Charles the Bald was said to resemble his grandfather physically (BNC HPT 175). This study compares data from translated texts against the background of original OE writings, establishing dependencies and differences between the two. Although the contrastive analysis of source and target texts is one of the major methods employed in the study, translation and translation strategies as such are only my secondary foci. The emphasis is rather on what source/target comparison can tell us about the OE non-finite syntax and the typological differences between Latin and OE in this domain, and on whether contact-induced change can originate in translation. In terms of theoretical framework, I have adopted functional-typological approach, which rests on the principles of iconicity and event integration, and to the best of my knowledge, has not been applied systematically to OE non-finite constructions. Therefore one more aim of the dissertation is to test this framework and to see how OE fits into the cross-linguistic picture of non-finites. My research corpus consists of two samples: 1) written OE closely dependent on the Latin originals, based on editions of two gloss texts, five translations, and Latin originals of these texts, representing four text types: hymns, religious regulations, homily/life narrative, and biblical narrative (180,622 words); and 2) written OE as far independent from Latin as possible, based on a selection from the York-Toronto-Helsinki Parsed Corpus of Old English Prose (YCOE) and representing five text types: laws, charters, correspondence, chronicle narrative, and homily/life narrative (274,757 words).

Use of non-specific and specific interactions in the analysis of testosterone and related compounds by capillary electromigration techniques

Determination of testosterone and related compounds in body fluids is of utmost importance in doping control and the diagnosis of many diseases. Capillary electromigration techniques are a relatively new approach for steroid research. Owing to their electrical neutrality, however, separation of steroids by capillary electromigration techniques requires the use of charged electrolyte additives that interact with the steroids either specifically or non-specifically. The analysis of testosterone and related steroids by non-specific micellar electrokinetic chromatography (MEKC) was investigated in this study. The partial filling (PF) technique was employed, being suitable for detection by both ultraviolet spectrophotometry (UV) and electrospray ionization mass spectrometry (ESI-MS). Efficient, quantitative PF-MEKC UV methods for steroid standards were developed through the use of optimized pseudostationary phases comprising surfactants and cyclodextrins. PF-MEKC UV proved to be a more sensitive, efficient and repeatable method for the steroids than PF-MEKC ESI-MS. It was discovered that in PF-MEKC analyses of electrically neutral steroids, ESI-MS interfacing sets significant limitations not only on the chemistry affecting the ionization and detection processes, but also on the separation. The new PF-MEKC UV method was successfully employed in the determination of testosterone in male urine samples after microscale immunoaffinity solid-phase extraction (IA-SPE). The IA-SPE method, relying on specific interactions between testosterone and a recombinant anti-testosterone Fab fragment, is the first such method described for testosterone. Finally, new data for interactions between steroids and human and bovine serum albumins were obtained through the use of affinity capillary electrophoresis. A new algorithm for the calculation of association constants between proteins and neutral ligands is introduced.