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

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) Lévy processes on half spaces for all t> 0. These Lévy processes may or may not have Gaussian component. When Lévy density is comparable to a decreasing function with damping exponent β, our estimate is explicit in terms of the distance to the boundary, the Lévy exponent and the damping exponent β of Lévy density.