Boundary Harnack inequality for α-harmonic functions on the Sierpiński triangle

Abstrakt

We prove a uniform boundary Harnack inequality for nonnegative functions harmonic with respect to _-stable process on the Sierpiński triangle, where α ∈ 0, 1. Our result requires no regularity assumptions on the domain of harmonicity.
2000 AMS Mathematics Subject Classification: Primary: 60J45.