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Extrapolation in the 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 consider some of the classical operators of harmonic analysis: convolution operators, singular integral operators, and Riesz potentials. Rather than treat each operator separately, we develop a general theory that builds upon the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The advantage of this approach is that it quickly yields sufficient conditions for these operators to be bounded on variable Lebesgue spaces; moreover, it can be applied to many other operators as well.

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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

Authors
  1. David V. Cruz-Uribe
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  2. Alberto Fiorenza
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Cruz-Uribe, D.V., Fiorenza, A. (2013). Extrapolation in the Variable Lebesgue Spaces. In: Variable Lebesgue Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0548-3_5

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