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Potential theory of one-dimensional geometric stable processes

Tomasz GrzywnyMichał Ryznar — 2012

Colloquium Mathematicae

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 α ∈ (0,2]. This process has an infinitesimal generator of the form - l o g ( 1 + ( - Δ ) α / 2 ) . As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.

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