Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components

摘要

In this paper, we derive explicit sharp two-sided estimates for the Dirichletheat kernels, in C^{1,1} open sets D in R^d, of a large class of subordinateBrownian motions with Gaussian components. When D is bounded, our sharptwo-sided Dirichlet heat kernel estimates hold for all t>0. Integrating theheat kernel estimates with respect to the time variable t, we obtain sharptwo-sided estimates for the Green functions, in bounded C^{1,1} open sets, ofsuch subordinate Brownian motions with Gaussian components.