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The maximal operator on weighted variable Lebesgue spaces

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Abstract

We study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces L p(·) ω (Ω). For a given log-Hölder continuous exponent p with 1 < inf p ⩽ supp < ∞ we present a necessary and sufficient condition on the weight ω for the boundedness of M. This condition is a generalization of the classical Muckenhoupt condition.

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Authors and Affiliations

  1. Department of Mathematics, Trinity College, 300 Summit St., Hartford, CT, 06106 - 3100, USA

    David Cruz-Uribe

  2. Institute of Mathematics, LMU Munich, (Ludwig-Maximilians-Universität München), Theresienstr. 39, D - 80333, Munich, Germany

    Lars Diening

  3. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FI - 90014, Oulu, Finland

    Peter Hästö

Authors
  1. David Cruz-Uribe
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  2. Lars Diening
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  3. Peter Hästö
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Correspondence to David Cruz-Uribe.

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Dedicated to Prof. Stefan Samko on the occasion of his 70th Anniversary

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Cruz-Uribe, D., Diening, L. & Hästö, P. The maximal operator on weighted variable Lebesgue spaces. fcaa 14, 361–374 (2011). https://doi.org/10.2478/s13540-011-0023-7

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