Geodesic
Harnack inequality for stable processes on $d$-sets
Krzysztof Bogdan 1   ; Andrzej Stós 1   ; Paweł Sztonyk 1
1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Studia Mathematica, Tome 158 (2003) no. 2, pp. 163-198 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We investigate properties of functions which are harmonic with respect to $\alpha $-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 the Boundary Harnack Principle.
DOI : 10.4064/sm158-2-5
Keywords: investigate properties functions which harmonic respect alpha stable processes d sets sierpi ski gasket carpet prove harnack inequality functions every process estimate its transition density harmonic measure ball prove continuity density harmonic measure results decay rate harmonic functions regular subsets d set the sierpi ski gasket even obtain boundary harnack principle

Krzysztof Bogdan  1   ; Andrzej Stós  1   ; Paweł Sztonyk  1

1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Krzysztof Bogdan; Andrzej Stós; Paweł Sztonyk. Harnack inequality for stable processes on $d$-sets. Studia Mathematica, Tome 158 (2003) no. 2, pp. 163-198. doi: 10.4064/sm158-2-5

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