Orlicz Spaces and Generalized Orlicz Spaces

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 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.

List of contents

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

Summary

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

• Authors: Petter Harjulehto, Petteri Harjulehto, Peter Hästö
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2019
• EAN: 9783030150990
• ISBN: 978-3-0-3015099-0
• No. of pages: 169
• Dimensions: 156 mm x 13 mm x 236 mm
• Weight: 283 g
• Illustrations: X, 169 p. 9 illus.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Differentialrechnung und -gleichungen, Funktionalanalysis und Abwandlungen, measure theory, Mathematics and Statistics, Functional Analysis, Real Functions, Partial Differential Equations, Differential calculus & equations, Functions of real variables, Functional analysis & transforms, Measure and Integration, Real analysis, real variables