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Abstract

We investigate properties of harmonic functions of the symmetric stable Lévy process on ${\mathbb R}^{d}$ without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman–Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for such functions.