Green function estimate for censored stable processes

Abstract

Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.