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 -norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-3,
author = {J. M. Aldaz and F. J. P\'erez L\'azaro},
title = {Regularity of the Hardy-Littlewood maximal operator on block decreasing functions},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {253-277},
zbl = {1175.42007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-3}
}
J. M. Aldaz; F. J. Pérez Lázaro. Regularity of the Hardy-Littlewood maximal operator on block decreasing functions. Studia Mathematica, Tome 192 (2009) pp. 253-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-3/