Pointwise estimates for densities of stable semigroups of measures
Studia Mathematica, Tome 104 (1993) no. 3, pp. 243-258
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let ${μ_t}$ be a symmetric α-stable semigroup of probability measures on a homogeneous group N, where 0 α 2. Assume that $μ_t$ are absolutely continuous with respect to Haar measure and denote by $h_t$ the corresponding densities. We show that the estimate $h_t(x) ≤ tΩ(x/|x|)|x|^{-n-α}$, 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 $ℳ f(x) = sup_{t>0} 1/t |ʃ_{0}^{t} h_{t-s} ∗ f ∗ h_s(x)ds|$ which, as is proved here, is of weak type (1,1).
@article{10_4064_sm_104_3_243_258,
author = {Pawe{\l} G{\l}owacki},
title = {Pointwise estimates for densities of stable semigroups of measures},
journal = {Studia Mathematica},
pages = {243--258},
publisher = {mathdoc},
volume = {104},
number = {3},
year = {1993},
doi = {10.4064/sm-104-3-243-258},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-104-3-243-258/}
}
TY - JOUR AU - Paweł Głowacki TI - Pointwise estimates for densities of stable semigroups of measures JO - Studia Mathematica PY - 1993 SP - 243 EP - 258 VL - 104 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-104-3-243-258/ DO - 10.4064/sm-104-3-243-258 LA - en ID - 10_4064_sm_104_3_243_258 ER -
Paweł Głowacki. Pointwise estimates for densities of stable semigroups of measures. Studia Mathematica, Tome 104 (1993) no. 3, pp. 243-258. doi: 10.4064/sm-104-3-243-258
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