Global Dirichlet Heat Kernel Estimates for Symmetric Lévy Processes in Half-Space

Abstract

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) Levy processes on half spaces for all t>0$t>0$. These Levy processes may or may not have Gaussian component. When Levy density is comparable to a decreasing function with damping exponent β$\beta$, our estimate is explicit in terms of the distance to the boundary, the Levy exponent and the damping exponent β$\beta$ of Levy density.