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Petteri Harjulehto, Peter Hästö (Beteiligte)

Orlicz Spaces and Generalized Orlicz Spaces


1st ed. 2019. 2019. x, 169 S. 9 SW-Abb. 235 mm
Verlag/Jahr: SPRINGER, BERLIN; SPRINGER INTERNATIONAL PUBLISHING 2019
ISBN: 3-03-015099-2 (3030150992)
Neue ISBN: 978-3-03-015099-0 (9783030150990)

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