University of Macau / Faculty of Science and Technology / Department of Mathematics

We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic setting and provide a molecular decomposition on Hardy spaces that will help facilitate the study of these operators. We extend two multiplier theorems, the first by Taibleson and Weiss and the second by Baernstein and Sawyer, to the anisotropic setting. Lastly, we characterize the Fourier transforms of Hardy spaces and show that all multipliers are necessarily continuous.

In this thesis we study the essential spectrum of composition operators on the Hardy space of the unit disc and of the upper half-plane. Our starting point is the spectral analysis of the composition operators induced by translations of the upper half-plane. We completely characterize the essential spectrum of a class of composition operators that are induced by perturbations of translations

In this thesis, we give a new definition of Hardy Spaces on hyperconvex domains in terms of Monge-Amp`ere measures which unifies the Hardy spaces on polydiscs and balls. Also we survey Monge-Amp`ere operators and Monge- Amp`ere measures.

In this thesis, we consider linear extremal problems in the Hp spaces. For many of these extremal problems, a unique solution can be guaranteed. We will examine some of the classical examples of extremal problems in these spaces. With this framework in place we will then consider a particular problem which does not always have a unique solution.

M.V. Cerrillo, W.H. Kautz. / "November 15, 1951." / Bibliography: p. 11. / Army Signal Corps Contract DA36-039 SC-64637 Project 102B. Dept. of the Army Projects 3-99-10-022 and DA3-99-10-000.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Daniel M. Oberlin, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

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Orientador: Jorge Tulio Mujica Ascui / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T23:05:35Z (GMT). No. of bitstreams: 1 Bertoloto_FabioJose_D.pdf: 716013 bytes, checksum: 13487be60bd9cd099898dc66a1234a32 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho, estudamos os já conhecidos espaços de Hardy de funções holomorfas Hp(Delta; F), 1 = p = 8. Estudamos também os espaços de Banach com as propriedades RNP e ARNP e os espaços UMD. Tendo introduzido estes, a partir de resultados voltados para o caso complexo dos artigos de Taylor [36], [37], que demonstram que (Hp(Delta ))' e Hq(Delta ) são canonicamente topologicamente isomorfos para 1 < p < 8, com q conjugado de p, demonstramos que sob as condições de F e F' terem a propridade ARNP, (Hp(Delta ; F))' e Hq(Delta ; F') são canonicamente topologicamente isomorfos (para 1 < p, q < 8, 1/p + 1 /q = 1) se, e somente se, F é UMD / Abstract: In this work we study the vector-valued Hardy spaces Hp(Delta ; F) (1 = p = 8). We also study the Banach spaces with the properties ARNP and RNP and the UMD spaces. We also study the Banach spaces with the RNP and ARNP properties, and also the UMD spaces. By following the approach of Taylor [36],[37] in the scalar-valued case, we prove that, when F and F' have the ARNP property, when (Hp(Delta ; F))' and Hq(Delta ; F) are canonically topologically isomorphic (for 1 < p, q < 8, 1/ p + 1/ q = 1) if and only if F is UMD / Doutorado / Analise Funcional / Doutor em Matemática

Orientador: Jorge Tulio Mujica Ascui / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação / Made available in DSpace on 2018-08-04T04:15:50Z (GMT). No. of bitstreams: 1 Bertoloto_FabioJose_M.pdf: 1324259 bytes, checksum: f7fd3d37bfe8d06ad156b30761402bfe (MD5) Previous issue date: 2005 / Resumo: O principal objetivo deste trabalho é o estudo de certos espaços de Banach de funções analíticas no disco aberto unitário, conhecidos como espaços de Hardy. Um outro objetivo é o estudo das propriedades básicas de álgebras de Banach, com especial ênfase na álgebra do disco e na álgebra das funções analíticas e limitadas no disco aberto unitário / Abstract: The main objective of this work is the study of certain Banach spaces of analytic functions on the open unit disc, known as Hardy spaces. Another objective is the study of the basic properties of Banach algebras, with special emphasis in the disc algebra and the algebra of bounded analytic functions in the open unit disc / Mestrado / Matematica / Mestre em Matemática