Synopsis
There are many good texts on using maximal functions in harmonic analysis, but Kinnunen, Lehrbäck, and Vähäkangas felt that there was room for a source book gathering developments in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximations for Sobolev functions, Hardy's inequalities, and partial differential equations. A recurring theme throughout the book is self-improvement of uniform quantitative conditions, they say, and they restrict their attention to prototypes in Euclidean spaces to avoid extra complication. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
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Maximal Function Methods for Sobolev Spaces
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American Mathematical Society, 2022
ISBN 10: 1470465752
ISBN 13: 9781470465759
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Maximal Function Methods for Sobolev Spaces (Paperback)
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ISBN 10: 1470465752
ISBN 13: 9781470465759
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Paperback. Condition: new. Paperback. This book discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hoelder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed.The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations. Discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781470465759
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Maximal Function Methods for Sobolev Spaces
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Maximal Function Methods for Sobolev Spaces
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Maximal Function Methods for Sobolev Spaces (Mathematical Surveys and Monographs, 257)
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Maximal Function Methods for Sobolev Spaces
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ISBN 10: 1470465752
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Paperback. Condition: New. This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed.The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations. Seller Inventory # LU-9781470465759
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Maximal Function Methods for Sobolev Spaces (Mathematical Surveys and Monographs, 257)
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Maximal Function Methods for Sobolev Spaces
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Maximal Function Methods for Sobolev Spaces
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American Mathematical Society, US, 2022
ISBN 10: 1470465752
ISBN 13: 9781470465759
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Paperback. Condition: New. This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed.The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations. Seller Inventory # LU-9781470465759
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