Boundary Harnack Principle for Subordinate Brownian Motions

Abstract

We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-fat open set (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded $\kappa$-fat open sets with respect to these processes with their Euclidean boundary.