Green function for gradient perturbation of unimodal Lévy processes

Abstract

GREEN FUNCTION FOR GRADIENT PERTURBATION OF UNIMODAL LÉVY PROCESSESWe prove that the Green function of a generator of isotropic unimodal Lévy processes with the weak lower scaling order greater thanone and the Green function of its gradient perturbations are comparable for bounded smooth open sets if the drift function is from an appropriate Kato class.