Hardy Operators On Euclidean Spaces And Related Topics
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Hardy Operators On Euclidean Spaces And Related Topics
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Author : Shanzhen Lu
language : en
Publisher: World Scientific
Release Date : 2023-03-23
Hardy Operators On Euclidean Spaces And Related Topics 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 2023-03-23 with Mathematics categories.
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.
Metric Space Topology Examples Exercises And Solutions
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Author : Wing-sum Cheung
language : en
Publisher: World Scientific
Release Date : 2023-10-18
Metric Space Topology Examples Exercises And Solutions written by Wing-sum Cheung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Mathematics categories.
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:
Weighted Inequalities Of Hardy Type Second Edition
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Author : Lars-erik Persson
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-06-16
Weighted Inequalities Of Hardy Type Second Edition written by Lars-erik Persson and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-16 with Mathematics categories.
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.
Euclidean Structures And Operator Theory In Banach Spaces
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Author : Nigel J. Kalton
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-15
Euclidean Structures And Operator Theory In Banach Spaces written by Nigel J. Kalton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Mathematics categories.
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Selected Papers On Analysis And Related Topics
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Selected Papers On Analysis And Related Topics written by 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 2008 with Mathematics categories.
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.
Clifford Algebras In Analysis And Related Topics
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Author : John Ryan
language : en
Publisher: CRC Press
Release Date : 2018-03-09
Clifford Algebras In Analysis And Related Topics written by John Ryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Mathematics categories.
This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.
Dirac Operators In Analysis
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Author : John Ryan
language : en
Publisher: CRC Press
Release Date : 1999-01-06
Dirac Operators In Analysis written by John Ryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-06 with Mathematics categories.
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.
Weighted Inequalities Of Hardy Type
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Author : Alois Kufner
language : en
Publisher: World Scientific
Release Date : 2003
Weighted Inequalities Of Hardy Type written by Alois Kufner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Weighted Norm Inequalities And Related Topics
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Author : J. García-Cuerva
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Weighted Norm Inequalities And Related Topics written by J. García-Cuerva and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
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.
Clifford Algebras In Analysis And Related Topics
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Author : John Ryan
language : en
Publisher: CRC Press
Release Date : 1995-10-23
Clifford Algebras In Analysis And Related Topics written by John Ryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-23 with Mathematics categories.
This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.