Boundary Harnack Principle for Symmetric Stable Processes

In this paper we study potential-theoretic properties of the symmetric α-stable processes (0<α<2): establishing the boundary Harnack principle for ratios of α-harmonic functions on any open sets, identifying the Martin boundary with the Euclidean boundary for open sets with a certain interior fatness property, and extending earlier results on intrinsic ultracontractivity and the conditional gauge theorem to certain open sets.