Real Variable Theory Of Musielak Orlicz Hardy Spaces

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Real-Variable Theory of Musielak-Orlicz Hardy Spaces

Dachun Yang,Yiyu Liang,Luong Dang Ky
Real Variable Theory of Musielak Orlicz Hardy Spaces Book PDF

Author : Dachun Yang,Yiyu Liang,Luong Dang Ky
Publisher : Springer
Page : 476 pages
File Size : 49,6 Mb
Release : 2017-05-09
Category : Mathematics
ISBN : 9783319543611

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Real-Variable Theory of Musielak-Orlicz Hardy Spaces by Dachun Yang,Yiyu Liang,Luong Dang Ky Pdf

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko

Yinqin Li,Dachun Yang,Long Huang
Real Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko Book PDF

Author : Yinqin Li,Dachun Yang,Long Huang
Publisher : Springer Nature
Page : 663 pages
File Size : 40,8 Mb
Release : 2023-02-14
Category : Mathematics
ISBN : 9789811967887

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Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko by Yinqin Li,Dachun Yang,Long Huang Pdf

The real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.

Function Spaces and Inequalities

Pankaj Jain,Hans-Jürgen Schmeisser
Function Spaces and Inequalities Book PDF

Author : Pankaj Jain,Hans-Jürgen Schmeisser
Publisher : Springer
Page : 335 pages
File Size : 53,8 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789811061196

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Function Spaces and Inequalities by Pankaj Jain,Hans-Jürgen Schmeisser Pdf

This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Orlicz Spaces and Generalized Orlicz Spaces

Petteri Harjulehto,Peter Hästö
Orlicz Spaces and Generalized Orlicz Spaces Book PDF

Author : Petteri Harjulehto,Peter Hästö
Publisher : Springer
Page : 169 pages
File Size : 47,5 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030151003

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Orlicz Spaces and Generalized Orlicz Spaces by Petteri Harjulehto,Peter Hästö Pdf

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series

Lars-Erik Persson,George Tephnadze,Ferenc Weisz
Martingale Hardy Spaces and Summability of One Dimensional Vilenkin Fourier Series Book PDF

Author : Lars-Erik Persson,George Tephnadze,Ferenc Weisz
Publisher : Springer Nature
Page : 633 pages
File Size : 47,8 Mb
Release : 2022-11-22
Category : Mathematics
ISBN : 9783031144592

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Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series by Lars-Erik Persson,George Tephnadze,Ferenc Weisz Pdf

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.

Lebesgue Points and Summability of Higher Dimensional Fourier Series

Ferenc Weisz
Lebesgue Points and Summability of Higher Dimensional Fourier Series Book PDF

Author : Ferenc Weisz
Publisher : Springer Nature
Page : 299 pages
File Size : 42,9 Mb
Release : 2021-06-12
Category : Mathematics
ISBN : 9783030746360

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Lebesgue Points and Summability of Higher Dimensional Fourier Series by Ferenc Weisz Pdf

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

Hardy Spaces on Homogeneous Groups

Gerald B. Folland,Elias M. Stein
Hardy Spaces on Homogeneous Groups Book PDF

Author : Gerald B. Folland,Elias M. Stein
Publisher : Princeton University Press
Page : 302 pages
File Size : 41,7 Mb
Release : 1982-06-21
Category : Mathematics
ISBN : 069108310X

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Hardy Spaces on Homogeneous Groups by Gerald B. Folland,Elias M. Stein Pdf

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.

The E. M. Stein Lectures on Hardy Spaces

Steven G. Krantz
The E M Stein Lectures on Hardy Spaces Book PDF

Author : Steven G. Krantz
Publisher : Springer Nature
Page : 257 pages
File Size : 52,9 Mb
Release : 2023-02-09
Category : Mathematics
ISBN : 9783031219528

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The E. M. Stein Lectures on Hardy Spaces by Steven G. Krantz Pdf

​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.

Operator and Norm Inequalities and Related Topics

Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman
Operator and Norm Inequalities and Related Topics Book PDF

Author : Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman
Publisher : Springer Nature
Page : 822 pages
File Size : 47,8 Mb
Release : 2022-08-10
Category : Mathematics
ISBN : 9783031021046

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Operator and Norm Inequalities and Related Topics by Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman Pdf

Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Theory of Besov Spaces

Yoshihiro Sawano
Theory of Besov Spaces Book PDF

Author : Yoshihiro Sawano
Publisher : Springer
Page : 945 pages
File Size : 50,5 Mb
Release : 2018-11-04
Category : Mathematics
ISBN : 9789811308369

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Theory of Besov Spaces by Yoshihiro Sawano Pdf

This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Operator Theory and Harmonic Analysis

Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Operator Theory and Harmonic Analysis Book PDF

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publisher : Springer Nature
Page : 585 pages
File Size : 43,7 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030774936

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Operator Theory and Harmonic Analysis by Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek Pdf

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

Gerald B. Folland,Elias M. Stein
Hardy Spaces on Homogeneous Groups MN 28 Volume 28 Book PDF

Author : Gerald B. Folland,Elias M. Stein
Publisher : Princeton University Press
Page : 302 pages
File Size : 43,7 Mb
Release : 2020-12-08
Category : Mathematics
ISBN : 9780691222455

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Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 by Gerald B. Folland,Elias M. Stein Pdf

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.

Operator Theory, Operator Algebras and Applications

M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky
Operator Theory Operator Algebras and Applications Book PDF

Author : M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky
Publisher : Springer
Page : 373 pages
File Size : 48,9 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9783034808163

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Operator Theory, Operator Algebras and Applications by M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky Pdf

This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).

New Trends in Applied Harmonic Analysis, Volume 2

Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
New Trends in Applied Harmonic Analysis Volume 2 Book PDF

Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 47,7 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530

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New Trends in Applied Harmonic Analysis, Volume 2 by Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter Pdf

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

Variable Lebesgue Spaces

David V. Cruz-Uribe,Alberto Fiorenza
Variable Lebesgue Spaces Book PDF

Author : David V. Cruz-Uribe,Alberto Fiorenza
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 51,6 Mb
Release : 2013-02-12
Category : Mathematics
ISBN : 9783034805483

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Variable Lebesgue Spaces by David V. Cruz-Uribe,Alberto Fiorenza Pdf

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.​