Orlicz Spaces and Generalized Orlicz Spaces [electronic resource] / by Petteri Harjulehto, Peter Hästö.
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TextSeries: Lecture Notes in Mathematics ; 2236Publisher: Cham : Springer International Publishing : Imprint: Springer, 2019Edition: 1st ed. 2019Description: X, 169 p. 9 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783030151003Subject(s): Measure theory | Functions of real variables | Functional analysis | Partial differential equations | Measure and Integration | Real Functions | Functional Analysis | Partial Differential EquationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.42 LOC classification: QA312-312.5Online resources: Click here to access online
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Springer eBooksSummary: 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.
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.