Orlicz Spaces and Generalized Orlicz Spaces

• Main Authors: Harjulehto, Petteri (Author, http://id.loc.gov/vocabulary/relators/aut), Hästö, Peter (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematics, 2236
• Subjects: Measure theory.; Functions of real variables.; Functional analysis.; Partial differential equations.; Measure and Integration.; Real Functions.; Functional Analysis.; Partial Differential Equations.
• Physical Description: X, 169 p. 9 illus. online resource.
• ISBN: 9783030151003
• ISSN: 0075-8434 ;
• DOI: 10.1007/978-3-030-15100-3

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.