The E M Stein Lectures On Hardy Spaces

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The E M Stein Lectures On Hardy Spaces

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Author : Steven G. Krantz
language : en
Publisher: Springer Nature
Release Date : 2023-02-09

The E M Stein Lectures On Hardy Spaces written by Steven G. Krantz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Mathematics categories.

​The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings. This book is based on Steven G. Krantz’s notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974. This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.

Four Lectures On Real Hp Spaces

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Author : Shanzhen Lu
language : en
Publisher: World Scientific
Release Date : 1995

Four Lectures On Real Hp Spaces written by Shanzhen Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

This book introduces the real variable theory of HP spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman-Stein on real HP spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real HP spaces. In addition, the dual spaces of real HP spaces, the interpolation of operators in HP spaces, and the interpolation of HP spaces are also discussed in Chapter 2. The properties of several basic operators in HP spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak HP spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in HP spaces, and the transference theorem of HP-multipliers etc. The last chapter is devoted to applications of real HP spaces to approximation theory.

Hardy Spaces On Ahlfors Regular Quasi Metric Spaces

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Author : Ryan Alvarado
language : en
Publisher: Springer
Release Date : 2015-06-09

Hardy Spaces On Ahlfors Regular Quasi Metric Spaces written by Ryan Alvarado and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-09 with Mathematics categories.

Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into two main parts, with the first part providing atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.

Hardy Spaces On The Euclidean Space

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Author : Akihito Uchiyama
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-01

Hardy Spaces On The Euclidean Space written by Akihito Uchiyama and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-01 with Mathematics categories.

Uchiyama's decomposition of BMO functions is considered the "Mount Everest of Hardy space theory". This book is based on the draft, which the author completed before his sudden death in 1997. Nowadays, his contributions are extremely influential in various fields of analysis, leading to further breakthroughs.

Summability Of Multi Dimensional Fourier Series And Hardy Spaces

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Author : Ferenc Weisz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Summability Of Multi Dimensional Fourier Series And Hardy Spaces written by Ferenc Weisz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].

Hardy Spaces On Homogeneous Groups

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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 2020-12-08

Hardy Spaces On Homogeneous Groups written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-08 with Mathematics categories.

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Lectures On Hermite And Laguerre Expansions

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Author : Sundaram Thangavelu
language : en
Publisher: Princeton University Press
Release Date : 1993-05-09

Lectures On Hermite And Laguerre Expansions written by Sundaram Thangavelu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-05-09 with Mathematics categories.

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

Anisotropic Hardy Spaces And Wavelets

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Author : Marcin Bownik
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Anisotropic Hardy Spaces And Wavelets written by Marcin Bownik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.

Harmonic Analysis In China

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Author : Minde Cheng
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Harmonic Analysis In China written by Minde Cheng and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Harmonic Analysis in China is a collection of surveys and research papers written by distinguished Chinese mathematicians from within the People's Republic of China and expatriates. The book covers topics in analytic function spaces of several complex variables, integral transforms, harmonic analysis on classical Lie groups and manifolds, LP- estimates of the Cauchy-Riemann equations and wavelet transforms. The reader will also be able to trace the great influence of the late Professor Loo-keng Hua's ideas and methods on research into harmonic analysis on classical domains and the theory of functions of several complex variables. Western scientists will thus become acquainted with the unique features and future trends of harmonic analysis in China. Audience: Analysts, as well as engineers and physicists who use harmonic analysis.

Explorations In Harmonic Analysis

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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-24

Explorations In Harmonic Analysis written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-24 with Mathematics categories.

This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.