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Structure of Variable Lebesgue Spaces

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Variable Lebesgue Spaces

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

In this chapter we give a precise definition of the variable Lebesgue spaces and establish their structural properties as Banach function spaces. Throughout this chapter we will generally assume that \(\Omega \) is a Lebesgue measurable subset of \({\mathbb{R}}^{n}\) with positive measure. Occasionally we will have to assume more, but we make it explicit if we do.

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Authors and Affiliations

  1. Department of Mathematics, Trinity College, Hartford, Connecticut, USA

    David V. Cruz-Uribe

  2. Dipartimento di Architettura, Università di Napoli “Federico II”, Napoli, Italy

    Alberto Fiorenza

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  1. David V. Cruz-Uribe
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  2. Alberto Fiorenza
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Cruz-Uribe, D.V., Fiorenza, A. (2013). Structure of Variable Lebesgue Spaces. In: Variable Lebesgue Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0548-3_2

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