Boundary Harnack Inequality for alpha-harmonic functions on the Sierpi\'nski triangle

TL;DR

This paper establishes a boundary Harnack inequality for alpha-harmonic functions on the Sierpiński triangle, applicable without domain regularity assumptions, advancing understanding of harmonic analysis on fractals.

Contribution

It proves a uniform boundary Harnack inequality for alpha-stable processes on the Sierpiński triangle without regularity constraints.

Findings

Boundary Harnack inequality holds for alpha-harmonic functions.

No regularity assumptions needed on the domain.

Results apply to all alpha in (0,1).

Abstract

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