Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation

In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C^1,1 open sets, as well as stable processes with drifts in bounded C^1,1 open sets. These twosided estimates are explicit involving distance functions to the boundary.