Green function for gradient perturbation of unimodal Lévy processes in the real line

Abstract

We prove that the Green function of a generator of symmetric unimodal Lévy processes with the weak lower scaling order bigger than one and the Green function of its gradient perturbations are comparable for bounded $C^{1,1}$ subsets of the real line if the drift function is from an appropriate Kato class.

arXiv admin note: text overlap with arXiv:1505.07700