Some properties of $\alpha$-harmonic measure

Volume 111 / 2008

Dimitrios Betsakos Colloquium Mathematicum 111 (2008), 297-314 MSC: 31B15, 31C05. DOI: 10.4064/cm111-2-8

Abstract

The $\alpha$-harmonic measure is the hitting distribution of symmetric $\alpha$-stable processes upon exiting an open set in ${\mathbb R}^n$ ($0<\alpha<2$, $n\geq 2$). It can also be defined in the context of Riesz potential theory and the fractional Laplacian. We prove some geometric estimates for $\alpha$-harmonic measure.

Authors

  • Dimitrios BetsakosDepartment of Mathematics
    Aristotle University of Thessaloniki
    54124 Thessaloniki, Greece
    e-mail

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