Boundary Harnack Principle for Symmetric Stable Processes

摘要

In this paper we study potential-theoretic properties of the symmetric #alpha#-stable processes (0 < #alpha# < 2): establishing the boundary Harnack principle for ratios of #alpha#-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.