Boundary Harnack principle for subordinate Brownian motions

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κκ-fat open sets (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 κκ-fat open sets with respect to these processes with their Euclidean boundaries.