Orlicz Spaces and Generalized Orlicz Spaces

ISBN-13: 9783030150990 / Angielski / Miękka / 2019 / 169 str.

Petteri Harjulehto; Peter Hasto

Spis treści

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

Blurb

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.