Displaying similar documents to “Some properties of α-harmonic measure”

Harnack inequality for stable processes on d-sets

Krzysztof Bogdan, Andrzej Stós, Paweł Sztonyk (2003)

Studia Mathematica

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We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain...