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Gradient estimates for the fundamental solution of Lévy type operator. (English) Zbl 1434.60207

Summary: We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of \(\alpha\)-stable type operators with \(\alpha \in (0, 1)\), which improve known results in the literature where the condition \(\alpha > 1/2\) is commonly assumed.

MSC:

60J35 Transition functions, generators and resolvents
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J76 Jump processes on general state spaces
60J45 Probabilistic potential theory
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