Orlicz Spaces and Generalized Orlicz Spaces

Description

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. Front Matter ....Pages i-x Introduction (Petteri Harjulehto, Peter Hästö)....Pages 1-12 Φ-Functions (Petteri Harjulehto, Peter Hästö)....Pages 13-46 Generalized Orlicz Spaces (Petteri Harjulehto, Peter Hästö)....Pages 47-78 Maximal and Averaging Operators (Petteri Harjulehto, Peter Hästö)....Pages 79-103 Extrapolation and Interpolation (Petteri Harjulehto, Peter Hästö)....Pages 105-121 Sobolev Spaces (Petteri Harjulehto, Peter Hästö)....Pages 123-144 Special Cases (Petteri Harjulehto, Peter Hästö)....Pages 145-157 Back Matter ....Pages 159-169