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

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Aldaz J., Pérez Lázaro F.

Studia Mathematica

2009

tom 194

nr 3

253-277

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.

Ograniczanie wyników

1 Studia Mathematica

1 Aldaz J.

1 Pérez Lázaro F.

1 2009

Wyniki wyszukiwania

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