Hardy Operators Function Spaces And Embeddings
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Hardy Operators Function Spaces And Embeddings
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Author : David E Edmunds
language : en
Publisher: Springer
Release Date : 2014-01-15
Hardy Operators Function Spaces And Embeddings written by David E Edmunds and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Hardy Operators Function Spaces And Embeddings
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Author : David E. Edmunds
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Hardy Operators Function Spaces And Embeddings written by David E. Edmunds and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Eigenvalues Embeddings And Generalised Trigonometric Functions
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Author : Jan Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-23
Eigenvalues Embeddings And Generalised Trigonometric Functions written by Jan Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-23 with Education categories.
The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.
Function Spaces Of Logarithmic Smoothness Embeddings And Characterizations
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Author : Óscar Domínguez
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13
Function Spaces Of Logarithmic Smoothness Embeddings And Characterizations written by Óscar Domínguez 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 2023-02-13 with Mathematics categories.
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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.
Spectral Theory Function Spaces And Inequalities
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Author : B. Malcolm Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-06
Spectral Theory Function Spaces And Inequalities written by B. Malcolm Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-06 with Mathematics categories.
This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Function Spaces And Inequalities
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Author : Pankaj Jain
language : en
Publisher: Springer
Release Date : 2017-10-20
Function Spaces And Inequalities written by Pankaj Jain and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Mathematics categories.
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.
The Analysis And Geometry Of Hardy S Inequality
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Author : Alexander A. Balinsky
language : en
Publisher: Springer
Release Date : 2015-10-20
The Analysis And Geometry Of Hardy S Inequality written by Alexander A. Balinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
Function Spaces And Applications
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Author : David Eric Edmunds
language : en
Publisher: CRC Press
Release Date : 2000
Function Spaces And Applications written by David Eric Edmunds and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Developed from the proceedings an international conference held in 1997, Function Spaces and Applications presents the work of leading mathematicians in the vital and rapidly growing field of functional analysis.
Elliptic Differential Operators And Spectral Analysis
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Author : D. E. Edmunds
language : en
Publisher: Springer
Release Date : 2018-11-20
Elliptic Differential Operators And Spectral Analysis written by D. E. Edmunds and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-20 with Mathematics categories.
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.