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arXiv · 2403.03298

Fractional Laplacian with supercritical killings

Soobin Cho·Renming Song
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Abstract

In this paper, we study Feynman-Kac semigroups of symmetric $\alpha$-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form $b|x|^{-\beta}$, where $b>0$ and $\beta>\alpha$. We obtain two-sided estimates on the densities $p(t, x, y)$ of these semigroups for all $t>0$, along with estimates for the corresponding Green functions.

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Soobin Cho, Renming Song. 2024-03-05. Fractional Laplacian with supercritical killings. https://arxiv.org/abs/2403.03298

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