Regularity of the Hardy-Littlewood maximal operator on block decreasing functions
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1
Universidad Autónoma de Madrid
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2
Universidad de La Rioja
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ISSN: 0039-3223
Any de publicació: 2009
Volum: 194
Número: 3
Pàgines: 253-277
Tipus: Article
Altres publicacions en: Studia Mathematica
Resum
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.