Representation of harmonic functions with respect to subordinate Brownian motion

In this article we prove a representation formula for non-negative generalized harmonic functions with respect to a subordinate Brownian motion in a general open set D subset of R-d. We also study oscillation properties of quotients of Poisson integrals and prove that oscillation can be uniformly tamed. (C) 2021 Elsevier Inc. All rights reserved.