Titlebook: Orlicz Spaces and Generalized Orlicz Spaces; Petteri Harjulehto,Peter Hästö Book 2019 Springer Nature Switzerland AG 2019 Extrapolation.Ma

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0075-8434 nd 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..978-3-030-15099-0978-3-030-15100-3Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Orlicz Spaces and Generalized Orlicz Spaces978-3-030-15100-3Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Introduction,We hope that our tools and exposition will aid in generalizing further results from the variable exponent setting to the generalized Orlicz setting.

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Generalized Orlicz Spaces,In the previous chapter, we investigated properties of Φ-functions. In this chapter, we use them to derive results for function spaces defined by means of Φ-functions.

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Extrapolation and Interpolation,In this chapter, we develop two techniques which allow us to transfer results of harmonic analysis from one setting to another: extrapolation and interpolation.

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Sobolev Spaces,In this chapter we study Sobolev spaces with generalized Orlicz integrability. We point out the novelties in this new setting and assume that the readers are familiar with classical Sobolev spaces.