Boundary Harnack Inequality for alpha-harmonic functions on the Sierpiński triangle

Abstract

We prove an uniform boundary Harnack inequality for nonnegative functions harmonic with respect to $\alpha$-stable process on the Sierpi{ń}ski triangle, where $\alpha \in (0,1)$. Our result requires no regularity assumptions on the domain of harmonicity.

References in corpus (1)

• Estimates and structure of $\alpha$-harmonic functions