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Orlicz spaces and generalized Orlicz spaces

Author: Petteri Harjulehto; Peter Hästö
Publisher: Cham, Switzerland : Springer, 2019.
Series: Lecture notes in mathematics (Springer-Verlag), 2236.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Petteri Harjulehto; Peter Hästö
ISBN: 9783030151003 303015100X 3030150992 9783030150990 9783030151010 3030151018
OCLC Number: 1101618193
Description: 1 online resource (x, 169 pages) : illustrations.
Contents: 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 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
Series Title: Lecture notes in mathematics (Springer-Verlag), 2236.
Responsibility: Petteri Harjulehto, Peter Hästö.

Abstract:

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating -function.  Read more...

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