Orlicz Spaces and Generalized Orlicz Spaces

This book presents a systematic treatment of generalized Orlicz spaces (also known as MusielakOrlicz 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 CalderónZygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and SobolevPoincaré 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

Inhalt

• Introduction.- -Functions. - Generalized Orlicz Spaces. - Maximal and Averaging Operators. - Extrapolation and Interpolation. - Sobolev Spaces. - Special Cases.