Orlicz Spaces and Generalized Orlicz Spaces

by Petteri Harjulehto, Peter Hïstï

Overview

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.

Product Details

ISBN-13:	9783030150990
Publisher:	Springer International Publishing
Publication date:	05/08/2019
Series:	Lecture Notes in Mathematics , #2236
Edition description:	1st ed. 2019
Pages:	169
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

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