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Hardy Operators On Euclidean Spaces And Related Topics
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Book Synopsis Hardy Operators On Euclidean Spaces And Related Topics by : Shanzhen Lu
Download or read book Hardy Operators On Euclidean Spaces And Related Topics written by Shanzhen Lu and published by World Scientific. This book was released on 2023-03-23 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many branches of mathematical analysis and mathematical physics, the Hardy operator and Hardy inequality are fundamentally important and have been intensively studied ever since the pioneer researches. This volume presents new properties of higher-dimensional Hardy operators obtained by the authors and their collaborators over the last decade. Its prime focus is on higher-dimensional Hardy operators that are based on the spherical average form.The key motivation for this monograph is based on the fact that the Hardy operator is generally smaller than the Hardy-Littlewood maximal operator, which leads to, on the one hand, the operator norm of the Hardy operator itself being smaller than the latter. On the other hand, the former characterizing the weight function class or function spaces is greater than the latter.
Book Synopsis Hardy Spaces on the Euclidean Space by : Akihito Uchiyama
Download or read book Hardy Spaces on the Euclidean Space written by Akihito Uchiyama and published by Springer Science & Business Media. This book was released on 2001-07-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Metric Space Topology: Examples, Exercises And Solutions by : Wing-sum Cheung
Download or read book Metric Space Topology: Examples, Exercises And Solutions written by Wing-sum Cheung and published by World Scientific. This book was released on 2023-10-18 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.The learning outcomes include:
Book Synopsis Weighted Inequalities of Hardy Type by : Alois Kufner
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific. This book was released on 2003 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Book Synopsis Hardy Operators, Function Spaces and Embeddings by : David E. Edmunds
Download or read book Hardy Operators, Function Spaces and Embeddings written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2004-07-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.
Author :Ruben A. Martinez-Avendano Publisher :Springer Science & Business Media ISBN 13 :0387485783 Total Pages :230 pages Book Rating :4.3/5 (874 download)
Book Synopsis An Introduction to Operators on the Hardy-Hilbert Space by : Ruben A. Martinez-Avendano
Download or read book An Introduction to Operators on the Hardy-Hilbert Space written by Ruben A. Martinez-Avendano and published by Springer Science & Business Media. This book was released on 2007-03-12 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Book Synopsis Hardy Inequalities on Homogeneous Groups by : Michael Ruzhansky
Download or read book Hardy Inequalities on Homogeneous Groups written by Michael Ruzhansky and published by Springer. This book was released on 2019-07-02 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Book Synopsis Hardy Operators, Function Spaces and Embeddings by : David E Edmunds
Download or read book Hardy Operators, Function Spaces and Embeddings written by David E Edmunds and published by Springer. This book was released on 2014-01-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hardy Classes and Operator Theory by : Marvin Rosenblum
Download or read book Hardy Classes and Operator Theory written by Marvin Rosenblum and published by Courier Corporation. This book was released on 1997-01-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.
Book Synopsis Weighted Inequalities Of Hardy Type (Second Edition) by : Lars-erik Persson
Download or read book Weighted Inequalities Of Hardy Type (Second Edition) written by Lars-erik Persson and published by World Scientific Publishing Company. This book was released on 2017-06-16 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems.In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.
Book Synopsis Some Recent Results on Hardy Type Operators in Weighted Function Spaces and Related Topics by : Miroslav Krbec
Download or read book Some Recent Results on Hardy Type Operators in Weighted Function Spaces and Related Topics written by Miroslav Krbec and published by . This book was released on 1993 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Papers on Analysis and Related Topics by :
Download or read book Selected Papers on Analysis and Related Topics written by and published by American Mathematical Soc.. This book was released on 2008 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal 'Sugaku'. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
Book Synopsis Dirac Operators in Analysis by : John Ryan
Download or read book Dirac Operators in Analysis written by John Ryan and published by CRC Press. This book was released on 1999-01-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Book Synopsis Weighted Norm Inequalities and Related Topics by : J. García-Cuerva
Download or read book Weighted Norm Inequalities and Related Topics written by J. García-Cuerva and published by Elsevier. This book was released on 2011-08-18 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying thread of this book is the topic of Weighted Norm Inequalities, but many other related topics are covered, including Hardy spaces, singular integrals, maximal operators, functions of bounded mean oscillation and vector valued inequalities. The emphasis is placed on basic ideas; problems are first treated in a simple context and only afterwards are further results examined.
Book Synopsis Euclidean Structures and Operator Theory in Banach Spaces by : Nigel J. Kalton
Download or read book Euclidean Structures and Operator Theory in Banach Spaces written by Nigel J. Kalton and published by American Mathematical Society. This book was released on 2023-09-15 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Convergence and Summability of Fourier Transforms and Hardy Spaces by : Ferenc Weisz
Download or read book Convergence and Summability of Fourier Transforms and Hardy Spaces written by Ferenc Weisz and published by Birkhäuser. This book was released on 2017-12-27 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
Book Synopsis Qα Analysis on Euclidean Spaces by : Jie Xiao
Download or read book Qα Analysis on Euclidean Spaces written by Jie Xiao and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-03-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the fundamentals of Qα spaces and their relationships to Besov spaces, this book presents all major results around Qα spaces obtained in the past 16 years. The applications of Qα spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This self-contained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations.
