Sharp Estimates on the Dirichlet Heat Kernels of Subordinate Brownian Motions

A subordinate Brownian motion can be obtained by replacing the time parameter of a Brownian motion by an increasing Levy process (i.e.,subordinator). Subordinate Brownian motions are very important in various applications. In this talk, I will give a survey of some recent results in the study of subordinate Brownian motions. In particular, I will present results on sharp two-sided estimates of the Dirichletheat kernel estimates of subordinate Brownian motions.