Comptes Rendus
Harnack inequality for symmetric stable processes on fractals
Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 59-63.

We study nonnegative harmonic functions of symmetric α-stable processes on d-sets F. We prove the Harnack inequality for such functions when α∈(0,2/dw)∪(ds,2). Furthermore, we investigate the decay rate of harmonic functions and the Carleson estimate near the boundary of a region in F. In the particular case of natural cells in the Sierpiński gasket we also prove the boundary Harnack principle.

Nous présentons l'inégalité de Harnack pour les fonctions α-harmoniques sur d-ensembles. En particulier cas de cellule naturelle du triangle de Sierpiński nous obtenons le principe de Harnack à la frontiére. Nous donnons aussi une estimation de la vitesse de decroissance des fonctions α-harmoniques près de la frontière ainsi que l'estimation de Carleson.

Published online:
DOI: 10.1016/S1631-073X(02)02425-1

Krzysztof Bogdan 1; Andrzej Stós 1; Paweł Sztonyk 1

1 Institute of Mathematics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
     author = {Krzysztof Bogdan and Andrzej St\'os and Pawe{\l} Sztonyk},
     title = {Harnack inequality for symmetric stable processes on fractals},
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Krzysztof Bogdan; Andrzej Stós; Paweł Sztonyk. Harnack inequality for symmetric stable processes on fractals. Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 59-63. doi : 10.1016/S1631-073X(02)02425-1.

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