Geodesic
Regularity of the Hardy–Littlewood maximal operator on block decreasing functions
J. M. Aldaz1 ; F. J. Pérez Lázaro2
1Departamento de Matemáticas Universidad Autónoma de Madrid Cantoblanco 28049 Madrid, Spain
2Departamento de Matemáticas y Computación Universidad de La Rioja Edificio J. L. Vives Calle Luis de Ulloa s//n 26004 Logroño, Spain
Studia Mathematica, Tome 194 (2009) no. 3, pp. 253-277
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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.
DOI : 10.4064/sm194-3-3
Keywords: study hardy littlewood maximal operator defined via unconditional norm acting block decreasing functions uncentered maximal operator maps block decreasing functions special bounded variation functions integrable distributional derivatives improving their regularity special maximal operator defined ell infty norm averaging cubes result extends block decreasing functions bounded variation necessarily special

J. M. Aldaz  1   ; F. J. Pérez Lázaro  2

1 Departamento de Matemáticas Universidad Autónoma de Madrid Cantoblanco 28049 Madrid, Spain
2 Departamento de Matemáticas y Computación Universidad de La Rioja Edificio J. L. Vives Calle Luis de Ulloa s//n 26004 Logroño, Spain 
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J. M. Aldaz; F. J. Pérez Lázaro. Regularity of the Hardy–Littlewood
 maximal operator on block decreasing functions. Studia Mathematica, Tome 194 (2009) no. 3, pp. 253-277. doi: 10.4064/sm194-3-3

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