GREEN FUNCTION FOR GRADIENT PERTURBATION OF UNIMODAL
Abstract: We prove that the Green function of a generator of isotropic unimodal Lévy processes
with the weak lower scaling order greater than one 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.
2010 AMS Mathematics Subject Classification: Primary: 47A55, 60J50, 60J75, 47G20;
Keywords and phrases: Unimodal Lévy process, heat kernel, smooth domain, Green
function, gradient perturbation.