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" Orlicz spaces and generalized Orlicz spaces / "
Petteri Harjulehto, Peter Hästö.
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BL
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| Record Number
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861318
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| Main Entry
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Harjulehto, Petteri
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| Title & Author
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Orlicz spaces and generalized Orlicz spaces /\ Petteri Harjulehto, Peter Hästö.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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Lecture notes in mathematics,; 2236
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| Page. NO
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1 online resource (x, 169 pages) :: illustrations
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| ISBN
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3030150992
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: 303015100X
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: 3030151018
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: 9783030150990
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: 9783030151003
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: 9783030151010
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9783030150990
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Includes bibliographical references and index.
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| Contents
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3.2 Quasinorm and the Unit Ball Property3.3 Convergence and Completeness; 3.4 Associate Spaces; 3.5 Separability; 3.6 Uniform Convexity and Reflexivity; 3.7 The Weight Condition (A0) and Density of Smooth Functions; 4 Maximal and Averaging Operators; 4.1 The Local Continuity Condition (A1); 4.2 The Decay Condition (A2); 4.3 Maximal Operators; 4.4 Averaging Operators and Applications; 5 Extrapolation and Interpolation; 5.1 Weights and Classical Extrapolation; 5.2 Rescaling and Conditions (A0), (A1) and (A2); 5.3 Diagonal and Off-Diagonal Extrapolation; 5.4 Applications of Extrapolation
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5.5 Complex Interpolation6 Sobolev Spaces; 6.1 Basic Properties; 6.2 Poincaré Inequalities; 6.3 Sobolev Embeddings; 6.4 Density of Regular Functions; 7 Special Cases; 7.1 Variable Exponent Growth; 7.2 Double Phase Growth; 7.3 Other Conditions; 7.4 Orlicz Spaces; References; Index
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| Abstract
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This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielakâ#x80;#x93;Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderónâ#x80;#x93;Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolevâ#x80;#x93;Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
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Orlicz spaces.
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Orlicz spaces.
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| Dewey Classification
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515/.73
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| LC Classification
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QA323
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| Added Entry
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Hästö, Peter
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