Potential theory of one-dimensional geometric stable processes

Tom 129 / 2012

Tomasz Grzywny, Michał Ryznar Colloquium Mathematicum 129 (2012), 7-40 MSC: Primary 60J45. DOI: 10.4064/cm129-1-2

Streszczenie

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator of the form $-\log(1+(-{\mit\Delta})^{\alpha/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.

Autorzy

  • Tomasz GrzywnyInstitute of Mathematics and Computer Sciences
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Michał RyznarInstitute of Mathematics and Computer Sciences
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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