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Comptes Rendus Mathématique
Volume 335, n° 1
pages 59-63 (2002)
Doi : S1631-073X(02)02425-1
Received : 7 Mars 2002 ; 
Harnack inequality for symmetric stable processes on fractals
L'inégalité de Harnack pour les processus symétriques stables sur les fractals
 

Krzysztof Bogdan , Andrzej Stós , Paweł Sztonyk
Institute of Mathematics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland 

Note presented by Marc Yor

Abstract

We study nonnegative harmonic functions of symmetric -stable processes on d -sets F . We prove the Harnack inequality for such functions when (0,2/d w )(d s ,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. To cite this article: K. Bogdan et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 59-63.

The full text of this article is available in PDF format.
Résumé

Nous présentons l'inégalité de Harnack pour les fonctions -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 -harmoniques près de la frontière ainsi que l'estimation de Carleson. Pour citer cet article : K. Bogdan et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 59-63.

The full text of this article is available in PDF format.


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