Regularity of the Hardy–Littlewood maximal operator on block decreasing functions

Volume 194 / 2009

J. M. Aldaz, F. J. Pérez Lázaro Studia Mathematica 194 (2009), 253-277 MSC: Primary 42B25, 26B30. DOI: 10.4064/sm194-3-3

Abstract

We study the Hardy–Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the $\ell _\infty $-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.

Authors

  • J. M. AldazDepartamento de Matemáticas
    Universidad Autónoma de Madrid
    Cantoblanco
    28049 Madrid, Spain
    e-mail
  • F. J. Pérez LázaroDepartamento de Matemáticas
    y Computación
    Universidad de La Rioja
    Edificio J. L. Vives
    Calle Luis de Ulloa s//n
    26004 Logroño, Spain
    e-mail

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