BOUNDARY HARNACK INEQUALITY FOR
-HARMONIC FUNCTIONS
ON THE SIERPIŃSKI TRIANGLE
Kamil Kaleta
Mateusz Kwaśnicki
Abstract: We prove a uniform boundary Harnack inequality for nonnegative functions harmonic
with respect to
-stable process on the Sierpiński triangle, where
. Our result
requires no regularity assumptions on the domain of harmonicity.
2000 AMS Mathematics Subject Classification: Primary: 60J45.
Keywords and phrases: Sierpi ń ski triangle, boundary Harnack in-
equality, stable process.