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

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

2009-07-04

arxiv.org/abs/0907.0793v1

Probab. Math. Stat. 30(2) (2010), pp. 353-368

Mathematics

Probability

Scientific paper

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.

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