H P Spaces

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Introduction to Hp Spaces

Author : Paul Koosis
Publisher : Cambridge University Press
ISBN 13 : 0521455219
Total Pages : 316 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Introduction to Hp Spaces by : Paul Koosis

Download or read book Introduction to Hp Spaces written by Paul Koosis and published by Cambridge University Press. This book was released on 1998 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this well known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). The intention was to give the reader, assumed to know basic real and complex variable theory and a little functional analysis, a secure foothold in the basic theory, and to understand its applications in other areas. For this reason, emphasis is placed on methods and the ideas behind them rather than on the accumulation of as many results as possible. The second edition retains that intention, but the coverage has been extended. The author has included two appendices by V. P. Havin, on Peter Jones' interpolation formula, and Havin's own proof of the weak sequential completeness of L1/H1(0); in addition, numerous amendments, additions and corrections have been made throughout.

Four Lectures on Real Hp? Spaces

Author : Shanzhen Lu
Publisher : World Scientific
ISBN 13 : 9789810221584
Total Pages : 236 pages
Book Rating : 4.2/5 (215 download)

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Book Synopsis Four Lectures on Real Hp? Spaces by : Shanzhen Lu

Download or read book Four Lectures on Real Hp? Spaces written by Shanzhen Lu and published by World Scientific. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On the Interpolation of Analytic Families of Operators Acting on Hp Spaces

Author : Elias M. Stein
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis On the Interpolation of Analytic Families of Operators Acting on Hp Spaces by : Elias M. Stein

Download or read book On the Interpolation of Analytic Families of Operators Acting on Hp Spaces written by Elias M. Stein and published by . This book was released on 1957 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Weighted Hp Spaces

Author : José García-Cuerva
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Weighted Hp Spaces by : José García-Cuerva

Download or read book Weighted Hp Spaces written by José García-Cuerva and published by . This book was released on 1979 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The $H^p$ Spaces of an Annulus

Author : Donald Sarason
Publisher : American Mathematical Soc.
ISBN 13 : 0821812564
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The $H^p$ Spaces of an Annulus by : Donald Sarason

Download or read book The $H^p$ Spaces of an Annulus written by Donald Sarason and published by American Mathematical Soc.. This book was released on 1965 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Function Spaces

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
ISBN 13 : 0821840614
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Function Spaces by : Krzysztof Jarosz

Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

Fourier Analysis

Author : Javier Duoandikoetxea Zuazo
Publisher : American Mathematical Soc.
ISBN 13 : 9780821883846
Total Pages : 248 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Fourier Analysis by : Javier Duoandikoetxea Zuazo

Download or read book Fourier Analysis written by Javier Duoandikoetxea Zuazo and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, H1, BMO spaces, and the T1 theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform in higher dimensions. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between H1, BMO, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the T1 theorem, which has been of crucial importance in the field. This volume has been updated and translated from the original Spanish edition (1995). Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.

Banach Spaces of Analytic Functions.

Author : J. Baker
Publisher : Springer
ISBN 13 : 3540372628
Total Pages : 150 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Banach Spaces of Analytic Functions. by : J. Baker

Download or read book Banach Spaces of Analytic Functions. written by J. Baker and published by Springer. This book was released on 2006-11-15 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts

Pick Interpolation and Hilbert Function Spaces

Author : Jim Agler
Publisher : American Mathematical Soc.
ISBN 13 : 9780821883907
Total Pages : 332 pages
Book Rating : 4.8/5 (839 download)

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Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler

Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Soc.. This book was released on 2002 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $Hinfty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $Hinfty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider theinterpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem,and the hereditary functional calculus.

Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 140088389X
Total Pages : 312 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 by : Elias M. Stein

Download or read book Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Martingales in Banach Spaces

Author : Gilles Pisier
Publisher : Cambridge University Press
ISBN 13 : 1107137241
Total Pages : 591 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Martingales in Banach Spaces by : Gilles Pisier

Download or read book Martingales in Banach Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2016-06-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.

Banach Spaces of Analytic Functions

Author : Kenneth Hoffman
Publisher : Courier Corporation
ISBN 13 : 0486458741
Total Pages : 227 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Banach Spaces of Analytic Functions by : Kenneth Hoffman

Download or read book Banach Spaces of Analytic Functions written by Kenneth Hoffman and published by Courier Corporation. This book was released on 2007-02-27 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc. The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the factorization, and a brief description of the classical approach to the theorems of the first five chapters. The remainder of the book addresses the structure of various Banach spaces and Banach algebras of analytic functions in the unit disc. Enhanced with 100 challenging exercises, a bibliography, and an index, this text belongs in the libraries of students, professional mathematicians, as well as anyone interested in a rigorous, high-level treatment of this topic.

Library of Congress Subject Headings

Author : Library of Congress
Publisher :
ISBN 13 :
Total Pages : 1432 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Library of Congress Subject Headings by : Library of Congress

Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2003 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Analytic Function Spaces and their Applications

Author : Javad Mashreghi
Publisher : Springer Nature
ISBN 13 : 3031335724
Total Pages : 426 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Lectures on Analytic Function Spaces and their Applications by : Javad Mashreghi

Download or read book Lectures on Analytic Function Spaces and their Applications written by Javad Mashreghi and published by Springer Nature. This book was released on 2023-11-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.

Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces

Author : Ryan Alvarado
Publisher : Springer
ISBN 13 : 3319181327
Total Pages : 491 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces by : Ryan Alvarado

Download or read book Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces written by Ryan Alvarado and published by Springer. This book was released on 2015-06-09 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Hp Spaces

Author : Peter L. Duren
Publisher : Courier Dover Publications
ISBN 13 : 9780486411842
Total Pages : 0 pages
Book Rating : 4.4/5 (118 download)

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Book Synopsis Theory of Hp Spaces by : Peter L. Duren

Download or read book Theory of Hp Spaces written by Peter L. Duren and published by Courier Dover Publications. This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, interpolation theory, more. 1970 edition.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512884
Total Pages : 595 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.