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arXiv · 1809.02425

Heat kernel estimates of fractional Schrödinger operators with negative hardy potential

Tomasz Jakubowski·Jian Wang
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Abstract

We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schrödinger operator with negative Hardy potential $$Δ^{α/2} -λ|x|^{-α}$$ on $\RR^d$, where $α\in(0,d\wedge 2)$ and $λ>0$. The proof is purely analytical but elementary. In particular, for upper bounds of heat kernel we use the Chapman-Kolmogorov equation and adopt self-improving argument.

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Tomasz Jakubowski, Jian Wang. 2018-09-15. Heat kernel estimates of fractional Schrödinger operators with negative hardy potential. https://arxiv.org/abs/1809.02425

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