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arXiv · 1910.04242

Heat kernel bounds for nonlocal operators with singular kernels

Moritz Kassmann·Kyung-Youn Kim·Takashi Kumagai
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Abstract

We prove sharp two-sided bounds of the fundamental solution for an integro-differential operator of order $\alpha \in (0,2)$ that generates a $d$-dimensional Markov process. The corresponding Dirichlet form is comparable to that of $d$ independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the $d$-dimensional Lebesgue measure.

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Moritz Kassmann, Kyung-Youn Kim, Takashi Kumagai. 2019-10-09. Heat kernel bounds for nonlocal operators with singular kernels. https://arxiv.org/abs/1910.04242

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