This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating ?-function. It introduces and develops a technique centered on the use of equivalent ?-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.
ISBN: | 9783030150990 |
Publication date: | 8th May 2019 |
Author: | Petteri Harjulehto, Peter Hästö |
Publisher: | Springer an imprint of Springer International Publishing |
Format: | Paperback |
Pagination: | 169 pages |
Series: | Lecture Notes in Mathematics |
Genres: |
Integral calculus and equations Real analysis, real variables Functional analysis and transforms Differential calculus and equations |