Overview
- The first book on harmonic analysis in generalized Orlicz spaces
- Considers the most general class of F-functions, giving a systematic presentation of the use of equivalent F-functions to simplify proofs
- Includes non-doubling versions of most results and also more general results for the case of (non-generalized) Orlicz spaces
- Includes as special cases variable exponent and double phase growth
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2236)
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Table of contents (7 chapters)
Keywords
About this book
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–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 Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–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.
Authors and Affiliations
Bibliographic Information
Book Title: Orlicz Spaces and Generalized Orlicz Spaces
Authors: Petteri Harjulehto, Peter Hästö
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-15100-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-15099-0Published: 08 May 2019
eBook ISBN: 978-3-030-15100-3Published: 07 May 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 169
Number of Illustrations: 9 b/w illustrations
Topics: Measure and Integration, Real Functions, Functional Analysis, Partial Differential Equations