Orlicz Spaces and Generalized Orlicz Spaces
Title:
Orlicz Spaces and Generalized Orlicz Spaces
ISBN:
9783030151003
Personal Author:
Edition:
1st ed. 2019.
Publication Information New:
Cham : Springer International Publishing : Imprint: Springer, 2019.
Physical Description:
X, 169 p. 9 illus. online resource.
Series:
Lecture Notes in Mathematics, 2236
Abstract:
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.
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Language:
English