Dissertations / Theses on the topic 'Wagga Wagga'

In rural inland, south-eastern Australia, allergy to the fungus Alternaria is prevalent and an important risk factor for asthma. The aim of the thesis was to investigate the distribution and factors influencing allergens of Alternaria in the air. As airborne allergenic spores were thought to arise from harvesting of nearby crops, two towns with different agricultural practices were studied. Moree has two crop harvesting periods in summer and autumn whilst Wagga Wagga has one harvesting period in summer. Over two years, air was sampled daily in Wagga Wagga and Moree using Burkard traps. The reliability of measurements from a single site to represent the distribution of airborne concentrations of spores across each town was examined using data from three traps simultaneously, sited 2.0 to 4.9 km apart, over four weeks. Substantial intra-class correlation coefficients (ICC) were observed between the three sampling sites across both towns (ICC=0.52, 95% CI 0.30-0.71 to 0.76, 95% CI 0.61-0.87) when counts of Alternaria spores were relatively high. The correlation was poor when counts were low. Of more than 365 trap tapes examined, the two microscopic traverses strongly correlated for counts of Alternaria spores (ICC=0.95, 95% CI 0.94-0.96). Alternaria was detected in both towns throughout the two year period with peaks in spore concentrations reflecting the season of crop harvesting in each region. Individual exposure to spores was examined. Thirty three subjects (adults and children from nine families) wore nasal air samplers and personal air samplers both inside and outside their homes. The effects of activity, location, age on the inhalation of Alternaria spores and variation between individuals in the same environment were determined. Every subject inhaled Alternaria spores. Personal exposure to Alternaria in the home environment varied substantially between subjects. Levels of fungal spores inhaled were higher during periods of activity than during rest, and higher while subjects were outdoors than indoors. During outdoor activity, the number of Alternaria spores inhaled ranged from 4 to 794 (median 11) spores/hr. Sources of airborne spores was investigated by sampling air above wheat and cotton crops near the towns during harvesting and non-harvesting periods, in a grain and cotton seed storage shed, and a cotton gin. Substantially higher concentrations were detected above crops during harvesting periods compared to non-harvesting periods. Peaks were associated with harvesting and other activities where plants were manipulated. By regression analysis spore concentrations in both towns were modelled against those detected above crops and with weather variables. Only one crop sampling period (cotton harvest) independently correlated with concentrations in town. Analysis combining all data showed concentrations of spores above crops correlated with spore concentrations in the town when lagged by one day. Variables of rainfall and maximum temperature influenced concentrations in both towns, and wind direction in Wagga Wagga alone. Parents of asthmatic children were asked by questionnaire in which locations symptoms were provoked. Asthma was reported to be exacerbated at grain farms and with disturbance of local vegetation in town and home gardens. Nasal sampling confirmed that activities that disturbed dust or vegetation increased the inhalation of spores. The factors that release allergen from spores were determined in a modified Halogen immunoassay. Approximately 60% of spores released allergen, and the proportion was influenced by isolate, nutrient availability, viability, and not influenced by sunlight or culture age up to 21 days. Germinating the spores significantly increased the proportion that released total allergen and Alt a 1 (p<0.0001). Alt a 1 appears to be a minor contributor to the total allergen released from spores except when spores have germinated. Conclusions: People living in inland rural regions of Australia are exposed to substantial quantities of allergenic spores of Alternaria. Exposure is a highly personal event and is largely determined by disturbance of local vegetation releasing spores such as from nearby crops by wind, harvesting, slashing, transport and processing of produce, and from within town and home gardens. Most spores inhaled are likely to be allergenic, with potency potentially increasing with viability.

In rural inland, south-eastern Australia, allergy to the fungus Alternaria is prevalent and an important risk factor for asthma. The aim of the thesis was to investigate the distribution and factors influencing allergens of Alternaria in the air. As airborne allergenic spores were thought to arise from harvesting of nearby crops, two towns with different agricultural practices were studied. Moree has two crop harvesting periods in summer and autumn whilst Wagga Wagga has one harvesting period in summer. Over two years, air was sampled daily in Wagga Wagga and Moree using Burkard traps. The reliability of measurements from a single site to represent the distribution of airborne concentrations of spores across each town was examined using data from three traps simultaneously, sited 2.0 to 4.9 km apart, over four weeks. Substantial intra-class correlation coefficients (ICC) were observed between the three sampling sites across both towns (ICC=0.52, 95% CI 0.30-0.71 to 0.76, 95% CI 0.61-0.87) when counts of Alternaria spores were relatively high. The correlation was poor when counts were low. Of more than 365 trap tapes examined, the two microscopic traverses strongly correlated for counts of Alternaria spores (ICC=0.95, 95% CI 0.94-0.96). Alternaria was detected in both towns throughout the two year period with peaks in spore concentrations reflecting the season of crop harvesting in each region. Individual exposure to spores was examined. Thirty three subjects (adults and children from nine families) wore nasal air samplers and personal air samplers both inside and outside their homes. The effects of activity, location, age on the inhalation of Alternaria spores and variation between individuals in the same environment were determined. Every subject inhaled Alternaria spores. Personal exposure to Alternaria in the home environment varied substantially between subjects. Levels of fungal spores inhaled were higher during periods of activity than during rest, and higher while subjects were outdoors than indoors. During outdoor activity, the number of Alternaria spores inhaled ranged from 4 to 794 (median 11) spores/hr. Sources of airborne spores was investigated by sampling air above wheat and cotton crops near the towns during harvesting and non-harvesting periods, in a grain and cotton seed storage shed, and a cotton gin. Substantially higher concentrations were detected above crops during harvesting periods compared to non-harvesting periods. Peaks were associated with harvesting and other activities where plants were manipulated. By regression analysis spore concentrations in both towns were modelled against those detected above crops and with weather variables. Only one crop sampling period (cotton harvest) independently correlated with concentrations in town. Analysis combining all data showed concentrations of spores above crops correlated with spore concentrations in the town when lagged by one day. Variables of rainfall and maximum temperature influenced concentrations in both towns, and wind direction in Wagga Wagga alone. Parents of asthmatic children were asked by questionnaire in which locations symptoms were provoked. Asthma was reported to be exacerbated at grain farms and with disturbance of local vegetation in town and home gardens. Nasal sampling confirmed that activities that disturbed dust or vegetation increased the inhalation of spores. The factors that release allergen from spores were determined in a modified Halogen immunoassay. Approximately 60% of spores released allergen, and the proportion was influenced by isolate, nutrient availability, viability, and not influenced by sunlight or culture age up to 21 days. Germinating the spores significantly increased the proportion that released total allergen and Alt a 1 (p<0.0001). Alt a 1 appears to be a minor contributor to the total allergen released from spores except when spores have germinated. Conclusions: People living in inland rural regions of Australia are exposed to substantial quantities of allergenic spores of Alternaria. Exposure is a highly personal event and is largely determined by disturbance of local vegetation releasing spores such as from nearby crops by wind, harvesting, slashing, transport and processing of produce, and from within town and home gardens. Most spores inhaled are likely to be allergenic, with potency potentially increasing with viability.

John D. Wagg was a native of Ashe County, North Carolina and a Southern Methodist circuit minister active immediately before and during the Civil War. His surviving journal, sermons, and received letters allow us to employ him as a window into a particular time, place, and set of conditions. To facilitate this, selections from the Wagg documents have been transcribed, edited, and presented as a Web-based digital edition, the Digital John D. Wagg Papers. This edition is designed to work with many other editions of similarly narrow historical and geographical scope as one historical witness in a network of witnesses. We must draw from several varieties of documents in the John Wagg collection and from contextualizing historical scholarship to construct a history of Wagg as a product of and participant in his times. Born 8 July 1835, Wagg began keeping a journal in 1854 as he worked toward a degree in medicine at Jefferson, North Carolina, the Wagg family hometown. As a diarist he often explored the place of humanity in a God-made world, a theme that foreshadows his turn from medicine and entry into the itinerant ministry of the Methodist Episcopal Church, South in October 1858. Wagg spent the Civil War years preaching throughout western North Carolina and southwest Virginia, generally striving to keep his heavily Confederate-leaning politics from the pulpit. This lifestyle allows the Wagg Papers to bring an alternate point of view to any archive of Civil War documents consisting primarily of the letters of combatants.
Master of Arts

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The Wagga Tank Prospect is located in Central Western N.S. W, 125 km south of Cobar. The prospect is hosted by the Lower Devonian Mount Hope Group, a complex succession of sedimentary, felsic volcanic and comagmatic intrusive rocks representing the oldest division of the Cobar Supergroup in the Mount Hope area. The prospect is primarily a Pb and Zn deposit with minor Cu, Ag and significant Au. Gold values are highest within steeply dipping gossan shoots in the oxidised zone, while Pb and Zn values are highest in subvertical shoots of massive sulphide within the primary zone. Cu is concentrated as chalcocite, digenite and malachite at a zone of supergene enrichment. The primary mineralization occurs within a zone of intense tectonic brecciation and argillic alteration at a pronounced flexure along the steeply dipping contact between the volcaniclastic sequence and a siltstone - slate sequence. The mineralization can be divided into two categories on the basis of textural relationships, i.e. fine grained, crudely banded massive type sulphides and coarser grained vein type sulphides. The vein type sulphides are represented by varying proportions of pyrite, chalcopyrite, sphalerite and galena with rare inclusions of cubanite and pyrrhotite. The massive type sulphides show mineral abundances of pyrite>sphalerite>galena>>chalcopyri te. Fluid inclusion and chlorite data indicate that the mineralizing fluid reached temperatures of about 325°C. Sulphur isotope compositions of the sulphide minerals (delta 34S = 10 per mil) suggest that the sulphur originated from seawater SO4-2. Reduction of seawater SO4-2 to H2S was primarily by an inorganic process at elevated temperatures in a heated rock pile. Thermodynamic calculations suggest possible log f02 - pH constraints of about log f02 = -29. 5 to -31. 7 and pH = 3 to 4. 5 for the mineralizing fluid. The mineralization is considered to be of epigenetic hydrothermal origin. The hydrothermal fluid was probably derived from dewatering of the rock pile during metamorphism accompanying the major deformation. Sulphide precipitation occurred along a plane of high permeability produced by folding of adjacent beds with a contrasting competency. The prospect bears many similarities to the principal deposits in the Cobar area. Those deposits are typically narrow steeply plunging elongate bodies occurring along sheared or brecciated contacts between cleaved turbiditic siltstones and coarser clastic beds or felsic volcanics.
Thesis (B.Sc.(Hons)) -- University of Adelaide, School of Physical Sciences, 1987

This thesis follows the First World War generation from the Wagga Wagga district in southern New South Wales through the late nineteenth century to the mid-1930s. The environment in which Wagga’s soldiers grew up, their months or years in the army and their lives as returned men touch on the war’s most enduring themes. Wagga’s volunteers were the country men of AIF lore. Yet many earned their living in the same professions and occupations as city dwellers. While those who laboured on farms or worked as tradesmen might have been the bush men described by contemporaries like Charles Bean, a significant proportion of Wagga’s soldiers were not. Many of the local men who survived the war were profoundly affected. Some never recovered. But the evidence also indicates the breadth of returned soldiers’ involvement in the community. As well as the unemployed, the destitute, those who needed constant care and those who turned to crime, there were veterans who had jobs and families and managed to live what could be considered normal lives. Local war veterans who succeeded in business or politics, or who were active in community organisations, feature heavily in Wagga’s civic record, but most of the district’s returned men appear only fleetingly. While little of their personal and family lives can be gleaned from these sources, this absence is balanced by the often detailed and sometimes first-hand accounts of individuals’ circumstances in Repatriation Department files. Although these voluminous records are becoming better known they have not previously been used to inform an in-depth study of a single locale’s returned soldiers. The Government and civic records on Wagga combine to reveal the nuances that underlie the broader national story of the war and the AIF. On many important themes the district’s example suggests both the truth behind commonly accepted views and the extent to which they obscure a more complex reality.

This thesis is an anthropological study of community response towards HIV and AIDS in Indonesia. It sheds a light at the actions by groups of Warga Peduli AIDS (literary means local residents concerned about AIDS), in Bandung City, the capital of West Java Province, Indonesia. I applied ethnographic research to investigate the characteristics of the groups and its actions: the process to form the groups, the process to design and to plan the actions, the values which underpin and motivate the activists to set up actions, the meaning of this action for the activists, and the impact of the actions for the beneficiaries. The Warga Peduli AIDS groups in Bandung mostly pioneered by women, but it is actually groups which are open for all members of the community regardless their gender, age, and social status. The actions by these groups include participating in HIV and AIDS related events, meetings, and workshops, disseminating information about HIV and AIDS to neighbours, promoting anti-stigma and anti-discrimination to people living with HIV and AIDS, assisting neighbours who need to take HIV test, assisting neighbours who are HIV positive to access treatment and to access livelihood supports, and providing companionship to neighbours who are HIV positive. In their action, the activists are able to bring the HIV and AIDS issue closer to the community without increasing the stigma of the sufferers and in a way it effectively address the problem in their neighbourhood. The activists of this action stated their action underpinned by the value of silih asah-asih, and asuh (mutual learning, loving, and caring) which is rooted in the Sundanese, the native culture of West Java, and they are motivated by the responsibility of taking care of and help those in need, regardless the cause of their misfortune, a value rooted in both in culture and religion. Besides this, the women activists view their activism in Warga Peduli AIDS as their new and interesting arena, in which they have more space and opportunity to express their voice, skill, and expertise as member of the community. In this thesis, I argue that Warga Peduli AIDS demonstrates a complex form of community activism: health, social, women, religious, and cultural activism. It is not merely a form of community-based health action which demonstrates an ‘HIV community competency’, but a form of a social activism that is loaded with religious and cultural values and that have been brought to the fore in the context of HIV and AIDS situation in Indonesia which then demonstrate an Indonesian feature of HIV community competency. Drawing on the context of women’s movement in the post reform era in Indonesia, I suggest that this action vividly illustrates the typical form of women’s grass root activism in post-Reformasi era, in which women have more space and opportunity to redefine their role and to re-shape their identity in order to respond the timely issue at their own community.

The thesis is devoted to the study of weak-type, strong-type and maximal estimates for martingale transforms in the weighted context. We put a particular emphasis to the following two aspects of the subject: I. To identify the optimal dependence of the constants on Muckenhoupt's characteristics of the weights involved; II. To establish the results with the use of the Bellman function method. Our interest in I. stems from the applications in the PDEs. For example, the aforementioned dependence on the characteristic is related to the regularity of solutions to certain elliptic di erential equations; via extrapolation, this topic is also linked to sharpness of some other estimates. The motivation for II. comes from the unweighted setting, in which the Bellman function method has been developed very intensively during the last forty years. We expect that the special functions and the approach developed in the thesis can be applied in the study of related bounds in probability theory and harmonic analysis. It should be emphasized that the content of the thesis is quite technical. Even in the simpler unweighted setting the analysis of the special functions of two or three variables can be quite elaborate, as evidenced in many papers in the literature. The passage to the truly weighted context adds two extra variables to the picture and makes the calculations really involved at many places. In some cases these computations seem unavoidable, but for some estimates we manage to develop methods which enable signifcant simplifcation. The material is organized as follows. The next chapter has a preliminary character and contains some motivation, the description of the necessary background and notation. The main contribution has been placed in Chapters 2, 3, 4 and 5. Chapter 2 is concerned with the analysis of tight weighted strong-type (p, p) estimates (1 < p < ∞) for martingale transforms. The contents of this part is taken from the joint paper with R. Bañuelos and A. Osękowski [5]. Chapter 3 studies the tight weighted weak-type (p, p) estimates (1 < p < ∞) for martingale transforms. It is the most technical part of the thesis, the analysis of the Bellman function constructed there is quite intricate and rests on the careful investigation of appropriate 4×4 matrices. The material is taken from a joint work with A. Osękowski (in preparation). Chapter 4 is the continuation of Chapter 3 and contains the investigation of weighted weak-type (p, p) estimates in the endpoint case p = ∞. We have decided to insert the analysis in a separate chapter, since the arguments are different from those in Chapter 3 and exploit certain novel composition/extrapolation of simpler Bellman functions. The material is taken from the paper [12] written jointly with A. Osękowski. In the final part of the thesis, Chapter 5, we investigate weighted maximal L1 estimates for martingale transforms, which can be regarded as endpoint complements of the result from Chapter 2. The material is taken from the work [13]. We have tried to keep this thesis as self-contained as possible, providing unproved statements with convenient references.
Niniejsza rozprawa poświęcona jest zbadaniu nierówności słabego typu, silnego typu oraz nierówności maksymalnych dla transformat martyngałowych w kontekście ważonym. W szczególności interesują nas następujące dwa problemy: I. Zidentyfikowanie optymalnej zależności stałych od charakterystyki wagi; II. Uzyskanie wyników z wykorzystaniem metody Bellmana. Motywacją dla zbadania problemu I. są zastosowania w teorii równań różniczkowych cząstkowych. Wspomniana zależność od charakterystyki wagi jest powiązana z regularnością rozwiązań pewnych eliptycznych równań różniczkowych; jest ona również powiązana z optymalnością pewnych innych oszacowań. Powodem, dla którego istotna jest kwestia II. są nierówności bezwagowe, w których z powodzeniem korzystano z metody Bellmana w przeciągu ostatnich czterdziestu lat. Oczekujemy, że funkcje specjalne i argumentacja przedstawiona w rozprawie mogą zostać zastosowane także w badaniu pokrewnych problemów w rachunku prawdopodobieństwa i analizie harmonicznej. Należy podkreślić, że rozprawa jest miejscami dosyć techniczna. Nawet w prostszym przypadku bezwagowym, analiza pojawiających się funkcji specjalnych dwóch lub trzech zmiennych bywa złożona, co odzwierciedla wiele prac z tej dziedziny. Przejście do kontekstu ważonego dodaje dwie kolejne zmienne i sprawia, że dowody stają się bardzo skomplikowane. Czasami nie udało się nam uniknąć złożonych, technicznych rozważań, jednak w niektórych przypadkach dowód został znacząco uproszczony dzięki wykorzystaniu nowych konstrukcji i argumentów. Rozprawa jest zorganizowana w następujący sposób. Pierwszy rozdział ma wstępny charakter i zawiera motywację oraz niezbędne definicje. Główne wyniki są zamieszczone w Rozdziałach 2, 3, 4 oraz 5. Rozdział 2 poświęony jest analizie ważonych nierówności mocnego typu (p, p) dla transformat martyngałowych, gdzie 1 < p < ∞. Rozdział jest oparty na wynikach ze wspólnego artykułu z R. Bañuelosem i A. Osękowskim [5]. W Rozdziale 3 badamy ważone oszacowania słabego typu (p, p) dla transformat martyngałowych, gdzie 1 < p < ∞. Jest to najbardziej techniczna część rozprawy, analiza skonstruowanej funkcji Bellmana jest dość złożona i opiera się na precyzyjnej analizie rozmaitych macierzy 4 × 4. Wynik pochodzi ze wspólnej pracy z A. Osękowskim (w przygotowaniu). Rozdział 4 stanowi kontynuację Rozdziału 3 i zawiera analizę nierówności słabego typu (p, p) w przypadku krańcowym p = ∞. Zdecydowaliśmy się umieścić ten wynik w osobnym rozdziale, ponieważ zastosowana metoda różni się od tej w Rozdziale 3 i wykorzystuje pewne nowe złożenia/ekstrapolację za pomocą prostszych funkcji Bellmana. Rozdział opiera się na publikacji [12] napisanej wspólnie z A. Osękowskim. W ostatniej części pracy, Rozdziale 5, badamy ważoną nierówność maksymalną L1 dla transformat martyngałowych, którą można interpretować jako krańcowy przypadek wyniku z Rozdziału 2. Materiał zaczerpnięto z pracy [13].

Praca dotyczy wewnętrznych, osobowych uwarunkowań poczucia szczęścia. Wpisuje się w nurt poszukiwań empirycznych w obszarze psychologii pozytywnej, wskazujących zarówno na hedonistyczne (Kahnemann, Diener i Schwarz, 1999), jak i eudajmonistyczne wyznaczniki poczucia szczęścia (Seligman, 2011). Oparta jest o założenie, że subiektywne szczęście zależy od doświadczania różnych emocji pozytywnych – związanych zarówno z dotychczasowym życiem, jak i antycypowaną przyszłością (nadzieją). Kategoryzacja emocji oparta została o „Taksonomię ludzkich emocji” (Jarymowicz i Imbir, 2010), rozróżniającą emocje o genezie automatycznej (AUT) i refleksyjnej (RFL). Przyjęto, że stopień poczucia szczęścia ma związek z wagami przypisywanymi emocjom obu rodzajów. Zaplanowana została seria badań związanych z następującymi tezami: I. Poczucie szczęścia (jako zgeneralizowany stan afektywny) jest funkcją pozytywnych doświadczeń emocjonalnych wszelkiego rodzaju, dotyczących nie tylko przeszłości i teraźniejszości, ale także przyszłości – w postaci doświadczanej nadziei, jako emocjonalnego atrybutu powiązanego w umyśle z celami życiowymi; II. Przeżywanie emocji wszelkiego rodzaju oznacza doświadczanie nie tylko uniwersalnych emocji automatycznych (AUT), ale także zależnych od rozwoju osobowego emocji refleksyjnych (RFL) – doświadczanie tych ostatnich wymaga ukształtowania i przyjęcia za własne standardów aksjologicznych, odnoszonych zarówno do własnej osoby, jak i do dobra ogólnego. Sformułowane zostały pytania badawcze – o związek poczucia szczęścia z emocjami o genezie automatycznej i refleksyjnej, z deklarowanymi wagami przypisywanymi tym emocjom, z ukształtowaniem standardów aksjologicznych oraz z nadzieją przejawiającą się wielością wygenerowanych celów życiowych. Przeprowadzone zostały 4 badania, w których (na zasadach dobrowolności) udział wzięły osoby z wyższym wykształceniem, rekrutowane przez Internet (za pomocą portali społecznościowych) oraz studenci uczelni warszawskich. Przebadano łącznie 786 osób (609 kobiet) w wieku 18-56 lat. Wykorzystano techniki kwestionariuszowe – do pomiaru: poczucia szczęścia, ocen wag emocji różnych kategorii oraz generowania osobistych celów życiowych. W toku badań eksperymentalnych wzbudzane były różne emocje – za pomocą (1) zdań o treściach emocjonalnych (prezentowanych na ekranie komputera albo odczytywanych przez lektora), (2) przywoływania własnych doświadczeń emocjonalnych oraz (3) podprogowego eksponowania słów odnoszących się do różnych emocji (zastosowano zmodyfikowaną wersję paradygmatu afektywnego poprzedzania – por. Murphy i Zajonc, 1994). Wyniki okazały się spójne z większością postawionych hipotez. Chociaż osoby badane oceniały pozytywne emocje automatyczne jako ważniejsze dla ludzkiego poczucia szczęścia niż pozytywne emocje refleksyjne, to waga nadana tym drugim okazała się być w większym stopniu związana z deklarowanym poczuciem własnego szczęścia. Ponadto, najwyższy poziom szczęścia deklarowały te osoby, które wygenerowały stosunkowo dużo celów życiowych oraz przypisały emocjom refleksyjnym wagi stosunkowo wysokie, a najniższy – te osoby, które wygenerowały stosunkowo mało celów życiowych oraz stosunkowo nisko oceniły znaczenie emocji refleksyjnych. Ze wskaźnikami poziomu poczucia szczęścia związane były również przejawy posiadania wyartykułowanych standardów aksjologicznych. W jednym z badań okazało się, że osoby deklarujące relatywnie wysoki poziom poczucia szczęścia wykazały się niższym poziomem skłonności punitywnych (mierzonych stopniem radykalizmu pomysłów co do kar wobec sprawców wyjątkowo haniebnego czynu) niż osoby o relatywnie niskim poziomie poczucia szczęścia. Łącznie, otrzymane dane wskazują na duże znaczenie subiektywnego docenienia emocji refleksyjnych oraz przejawów wartościowania refleksyjnego dla poczucia szczęścia. Dane skłaniają do postulowania by uznać, że potoczne pojęcie „pełni szczęścia” warto powiązać z trzema testowanymi czynnikami: 1) doświadczaniem emocji zarówno AUT, jak i RFL, 2) przypisywaniem emocjom RFL stosunkowo wysokich wag, 3) doświadczaniem nadziei, powiązanej z artykułowanymi celami życiowymi.

The thesis is devoted to the study of various classes of inequalities for maximal operators, both in the weighted and the unweighted settings. It is distinguished by the following two features: I. We put a particular emphasis on obtaining sharp results, i.e., deriving the optimal values of the constants involved; II. We establish the results with the use of the Bellman function method. The motivation for I. comes from the fact that maximal operators provide an efficient tool for the study of wide classes of operators appearing in harmonic analysis. In particular, maximal estimates can often be applied to obtain the appropriate boundedness properties of such operators. From this perspective, II. is a very natural direction: Bellman function method is a tool which enables the investigation of extremal problems and optimal constants. We expect that the special functions and the unified approach presented in the thesis can be further extended and exploited in the study of related sharp bounds in probability theory and harmonic analysis. Throughout, we focus mainly on the dyadic maximal operators and their certain extensions, the so-called dyadic-like maximal operators, which have a direct interpretation in the probability theory. The material is organized as follows. Chapter 1 is of an introductory character and contains some motivation, necessary background information, and notation. Chapter 2 is devoted to the description of the Bellman function method, specified to the context of maximal estimates; this unified approach is a compilation of several works from the literature. The main contribution of the thesis has been placed in the next five chapters. In Chapter 3 we obtain a sharp weighted extension of the Kolmogorov inequality: a maximal Lp estimate for p < 1. Chapter 4 contains a proof of a transference theorem which enables the passage from a certain type of unweighted estimates for the dyadic maximal operator to their Fefferman-Stein counterparts in the dyadic-like context. Chapter 5 is devoted to a certain maximal weak-type estimate in the presence of Muckenhoupt’s Ap weights, p > 1. Chapter 6 deals with a sharp Lorentz-norm inequality for maximal functions. In the finalpart of the paper, Chapter 7, we establish a sharp two-weight bound for a slightly different object, the so-called harmonic maximal operator. The contents of the dissertation is quite technical, at least at some points. The search for the optimal constants and the use of the Bellman function method makes the calculations really involved in many cases.
Rozprawa jest poświęcona badaniu różnych klas nierówności dla operatorów maksymalnych, zarówno w kontekście ważonym jak i bezwagowym. Wyróżniają ją następujące dwie cechy: I. Kładziemy szczególny nacisk na otrzymywanie wyników z optymalną stałą; II. Stosujemy metodę funkcji Bellmana. Motywacja dla I. wynika z faktu, ze operatory maksymalne stanowią efektywne narzędzie do studiowania szerokich klas operatorów występujących w analizie harmonicznej. W szczególności, oszacowania maksymalne często mogą być stosowane do otrzymywania odpowiednich własności ograniczoności takich operatorów. Z tej perspektywy II. jest bardzo naturalnym kierunkiem: metoda funkcji Bellmana jest narzędziem pozwalającym na badanie problemów ekstremalnych z optymalnymi stałymi. Mamy nadzieję, że funkcje specjalne oraz zunifikowane podejście zaprezentowane w niniejszej rozprawie będą mogły być dalej uogólniane i wykorzystywane w pracy nad pokrewnymi nierównościami z optymalną stałą w teorii prawdopodobieństwa i analizie harmonicznej. W całej rozprawie skupiamy się głównie na diadycznych operatorach maksymalnych i na pewnym ich uogólnieniu, tak zwanych quasi-diadycznych operatorach maksymalnych, które ma bezpośrednią interpretację w probabilistyce. Praca jest zorganizowana w następujący sposób: Rozdział 1 ma charakter wprowadzający i zawiera motywacje, potrzebne informacje wstępne i notacje. Rozdział 2 jest poświęcony opisowi metody funkcji Bellmana w kontekście oszacowań maksymalnych; to zunifikowane podejście jest kompilacją kilku prac z literatury. Główny wkład niniejszej rozprawy umieściliśmy w następnych pięciu rozdziałach. W Rozdziale 3 otrzymujemy oszacowanie ważone z optymalną stałą będące uogólnieniem nierówności Kołmogorowa: nierówności maksymalnej w L p dla p < 1. Rozdział 4 zawiera dowód twierdzenia pozwalającego na przejście od pewnego typu oszacowań bezwagowych dla diadycznego operatora maksymalnego do ich odpowiedników typu Feffermana-Steina w kontekście quasi-diadycznym. Rozdział 5 jest poświęcony pewnej nierówności maksymalnej słabego typu z wagą klasy Ap Muckenhoupta, p > 1. W Rozdziale 6 zajmujemy się oszacowaniem z optymalną stałą dla norm Lorentza funkcji maksymalnych. W ostatniej części pracy, Rozdziale 7, dowodzimy nierówności dwuwagowej z optymalną stałą dla nieco innego obiektu, tak zwanego harmonicznego operatora maksymalnego. Zawartość rozprawy jest dość techniczna, przynajmniej w niektórych miejscach. Poszukiwanie optymalnych stałych i stosowanie metody funkcji Bellmana w wielu przypadkach wymaga skomplikowanych obliczeń.