Boundary potential theory for stable Lévy processes

Tom 95 / 2003

Paweł Sztonyk Colloquium Mathematicum 95 (2003), 191-206 MSC: Primary 60J45, 31C05; Secondary 60G51. DOI: 10.4064/cm95-2-4


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.


  • Paweł SztonykInstitute of Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland

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