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Pointwise estimates for densities of stable semigroups of measures

Paweł Głowacki, Waldemar Hebisch (1993)

Studia Mathematica

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 ) t Ω ( 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...

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