Orlicz Spaces and Generalized Orlicz Spaces

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· Springer
eBook
169
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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 ÎĶ-function. It introduces and develops a technique centered on the use of equivalent ÎĶ-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 CalderÃģn–Zygmund operators. Finally, central results are provided for Sobolev spaces, including PoincarÃĐ and Sobolev–PoincarÃĐ 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.


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