| We establish the boundary Harnack principle for certain classes of symmetric stable-like processes in Rd on arbitrary open sets as well as censored stable-like processes on C1,1- domains. Using those results, we derive Dirichlet heat kernel estimates for killed stable-like processes and killed censored stable-like processes in kappa-fat domains in terms of the surviving probabilities and the global transition density of the processes. For C 1,1-domains, we derive explicit estimates of the Dirichlet heat kernel. |
