Asymptotic behavior of densities of unimodal convolution semigroups

Abstract

We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on ${\mathbb{R}}^d$ under the assumption that its Lévy--Khintchine exponent is regularly varying of index between $0$ and $2$.

arXiv commentWe added Section 3; paper accepted in Transactions of AMS

References in corpus (3)

• On Harnack inequality and Hölder regularity for isotropic unimodal Lévy processes
• A note on the existence of transition probability densities for Lévy processes
• Asymptotic behaviour and estimates of slowly varying convolution semigroups

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• Optimal Hardy inequality for the fractional Laplacian on $L^p$