Potential Analysis

, Volume 17, Issue 1, pp 1–23

Estimates of Green Function for Relativistic α-Stable Process

  • MichaŁ Ryznar
Article

DOI: 10.1023/A:1015231913916

Cite this article as:
Ryznar, M. Potential Analysis (2002) 17: 1. doi:10.1023/A:1015231913916

Abstract

We call an Rd-valued stochastic process Xt with characteristic function exp {−t{(m2/α2)α/2m}},ξ∈Rd,m>0, the relativistic α-stable process. In the paper we derive sharp estimates for the Green function of the relativistic α-stable process on C1,1 domains. Using these estimates we provide lower and upper bounds for the Poisson kernel. As another application we derive 3G Theorem and Boundary Harnack Principle for C1,1 domains.

stable and relativistic stable processesGreen functionharmonic functionsPoisson kernel

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • MichaŁ Ryznar
    • 1
  1. 1.Institute of MathematicsWroclaw University of TechnologyWrocławPoland