Let be a symmetric α-stable semigroup of probability measures on a homogeneous group N, where 0 < α < 2. Assume that are absolutely continuous with respect to Haar measure and denote by the corresponding densities. We show that the estimate , x≠0, holds true with some integrable function Ω on the unit sphere Σ if and only if the density of the Lévy measure of the semigroup belongs locally to the Zygmund class LlogL(N╲e). The problem turns out to be related to the properties of the maximal function which, as is proved here, is of weak type (1,1).
@article{bwmeta1.element.bwnjournal-article-smv104i3p243bwm,
author = {Pawe\l\ G\l owacki and Waldemar Hebisch},
title = {Pointwise estimates for densities of stable semigroups of measures},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {243-258},
zbl = {0812.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p243bwm}
}
Głowacki, Paweł; Hebisch, Waldemar. Pointwise estimates for densities of stable semigroups of measures. Studia Mathematica, Tome 104 (1993) pp. 243-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p243bwm/
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