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

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 l_infty-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.

26 pages

References in corpus (1)

• Boundedness and unboundedness results for some maximal operators on functions of bounded variation

Cited by in corpus (5)

• Optimal bounds on the modulus of continuity of the uncentered Hardy-Littlewood maximal function
• On high dimensional maximal operators
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• The Variation of the Uncentered Maximal Operator with respect to Cubes
• Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures