Harnack inequality for stable processes on d-sets

• Autorzy: Krzysztof Bogdan , Andrzej Stós , Paweł Sztonyk
• Języki publikacji: EN

Abstrakty

EN

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 the Boundary Harnack Principle.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 60J45: Probabilistic potential theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 158
• Numer: 2
• Strony: 163-198

Daty

wydano

2003

Twórcy

autor

Krzysztof Bogdan

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Andrzej Stós

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Paweł Sztonyk

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm158-2-5