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Contents of PMS, Vol. 37, Fasc. 1,
pages 119 - 143
 

GREEN FUNCTION FOR GRADIENT PERTURBATION OF UNIMODAL LÉVY PROCESSES

Tomasz Grzywny
Tomasz Jakubowski
Grzegorz Żurek

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; Secondary: 60J35.

Keywords and phrases: Unimodal Lévy process, heat kernel, smooth domain, Green function, gradient perturbation.

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