Minimal thinness for subordinate Brownian motion in half-space

We study minimal thinness in the half-space H:= {x = (x̃, x _d): x̃ ∈ ℝ ^d-1,x _d > 0} for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of H below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.