Orlicz Spaces and Generalized Orlicz Spaces, 1st ed. 2019 Lecture Notes in Mathematics Series, Vol. 2236

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.

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