Boundary Harnack Principle for fractional powers of Laplacian on the   Sierpinski carpet
  We prove the Boundary Harnack Principle related to fractional powers of Laplacian for some natural regions in the two-dimensional Sierpinski carpet. This is a natual application of a probabilistic method based on the Ikeda-Watanabe formula 
Andrzej Stos (LMP-Clermont)