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

  1. Aldaz, J.M. 1
  2. Lázaro, F.J.P. 2
  1. 1 Universidad Autónoma de Madrid
    info

    Universidad Autónoma de Madrid

    Madrid, España

    ROR https://ror.org/01cby8j38

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revue:
Studia Mathematica

ISSN: 0039-3223

Année de publication: 2009

Volumen: 194

Número: 3

Pages: 253-277

Type: Article

DOI: 10.4064/SM194-3-3 SCOPUS: 2-s2.0-72149083315 WoS: WOS:000271388600003 GOOGLE SCHOLAR

D'autres publications dans: Studia Mathematica

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Résumé

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 l∞-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special. © Instytut Matematyczny PAN, 2009.