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arXiv · 1710.05478

On estimates of transition density for subordinate Brownian motions with Gaussian components in $C^{1,1}$-open sets

Joohak Bae·Panki Kim
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Abstract

We consider a subordinate Brownian motion $X$ with Gaussian components when the scaling order of purely discontinuous part is between $0$ and $2$ including $2$. In this paper we establish sharp two-sided bounds for transition density of $X$ in ${\mathbb R}^d$ and $C^{1,1}$-open sets. As a corollary, we obtain a sharp Green function estimates.

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Joohak Bae, Panki Kim. 2017-10-16. On estimates of transition density for subordinate Brownian motions with Gaussian components in $C^{1,1}$-open sets. https://arxiv.org/abs/1710.05478

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