Dirichlet Heat Kernel Estimates for Stable Processes with Singular Drift In Unbounded C^1,1 Open Sets

Suppose d ≥ 2 and α ∈ (1, 2). Let D be a (not necessarily bounded) C^1,1 open set in ℝ^d and μ = (μ¹, . . ., μ^d) where each μ^j is a signed measure on ℝ^d belonging to a certain Kato class of the rotationally symmetric α-stable process X. Let X^μ be an α-stable process with drift μ in ℝ^d and let X^μ,D be the subprocess of X^μ in D. In this paper, we derive sharp two-sided estimates for the transition density of X^μ,D.