Orlicz Spaces and Generalized Orlicz Spaces  (English, Paperback, Harjulehto Petteri)

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 Calderon-Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincare and Sobolev-Poincare 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.