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

J. M. Aldaz, and F. J. Pérez Lázaro. "Regularity of the Hardy-Littlewood maximal operator on block decreasing functions." Studia Mathematica 194.3 (2009): 253-277. <http://eudml.org/doc/284576>.

@article{J2009,
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 $ℓ_\{∞\}$-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.},
author = {J. M. Aldaz, F. J. Pérez Lázaro},
journal = {Studia Mathematica},
language = {eng},
number = {3},
pages = {253-277},
title = {Regularity of the Hardy-Littlewood maximal operator on block decreasing functions},
url = {http://eudml.org/doc/284576},
volume = {194},
year = {2009},
}

TY - JOUR
AU - J. M. Aldaz
AU - F. J. Pérez Lázaro
TI - Regularity of the Hardy-Littlewood maximal operator on block decreasing functions
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 3
SP - 253
EP - 277
AB - 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.
LA - eng
UR - http://eudml.org/doc/284576
ER -