Global heat kernel estimate for relativistic stable processes in exterior open sets (Q442187)

The main result of this paper is a sharp two-sided estimate for the transition densities of relativistic \(\alpha \)-stable processes with mass \(m\in (0,1]\) in \(C^{1,1}\)-exterior open sets valid for all times \(t>0\). These transition densities are also the Dirichlet heat kernels of \(m-(m^{2/\alpha } - \Delta )^{\alpha /2}\). Moreover, the estimates are uniform in \(m\) in the sense that the constants are independent of \(m\in (0,1]\). A sharp two-sided estimate for the corresponding Green function is deduced as a corollary of the main result.