Abstract
In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in $D$ whose scaling order is not necessarily strictly below $2$. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and the Laplace exponent of the corresponding subordinator only.
Citation
Panki Kim. Ante Mimica. "Estimates of Dirichlet heat kernels for subordinate Brownian motions." Electron. J. Probab. 23 1 - 45, 2018. https://doi.org/10.1214/18-EJP190
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