This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating F-function. It introduces and develops a technique centered on the use of equivalent F-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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
9
9 s/w Abbildungen
X, 169 p. 9 illus.
Dateigröße
ISBN-13
978-3-030-15100-3 (9783030151003)
DOI
10.1007/978-3-030-15100-3
Schweitzer Klassifikation
- Introduction.- F-Functions. - Generalized Orlicz Spaces. - Maximal and Averaging Operators. - Extrapolation and Interpolation. - Sobolev Spaces. - Special Cases.
