Hardy Operators On Euclidean Spaces And Related Topics PDF Download
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Author: Shanzhen Lu
Publisher: World Scientific
ISBN: 9811253692
Category : Mathematics
Languages : en
Pages : 215
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Book Description
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.
Author: Shanzhen Lu
Publisher: World Scientific
ISBN: 9811253692
Category : Mathematics
Languages : en
Pages : 215
Get Book
Book Description
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.
Author: Akihito Uchiyama
Publisher: Springer Science & Business Media
ISBN: 9784431703198
Category : Mathematics
Languages : en
Pages : 328
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Book Description
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.
Author: Wing-sum Cheung
Publisher: World Scientific
ISBN: 9811266999
Category : Mathematics
Languages : en
Pages : 442
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Book Description
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:
Author: David E. Edmunds
Publisher: Springer Science & Business Media
ISBN: 9783540219729
Category : Computers
Languages : en
Pages : 352
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Book Description
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: 0387485783
Category : Mathematics
Languages : en
Pages : 230
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Book Description
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.
Author: John Ryan
Publisher: CRC Press
ISBN: 1351460277
Category : Mathematics
Languages : en
Pages : 174
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Book Description
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.
Author: Marvin Rosenblum
Publisher: Courier Corporation
ISBN: 9780486695365
Category : Mathematics
Languages : en
Pages : 204
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Book Description
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.
Author: Alois Kufner
Publisher: World Scientific Publishing Company
ISBN: 9813140666
Category :
Languages : en
Pages : 480
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Book Description
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. Request Inspection Copy
Author: David E Edmunds
Publisher: Springer
ISBN: 9783662077320
Category :
Languages : en
Pages : 344
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Book Description
Author: Alois Kufner
Publisher: World Scientific
ISBN: 9789812381958
Category : Mathematics
Languages : en
Pages : 380
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Book Description
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.
