Displaying similar documents to “Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian”

Some properties of α-harmonic measure

Dimitrios Betsakos (2008)

Colloquium Mathematicae

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The α-harmonic measure is the hitting distribution of symmetric α-stable processes upon exiting an open set in ℝⁿ (0 < α < 2, n ≥ 2). It can also be defined in the context of Riesz potential theory and the fractional Laplacian. We prove some geometric estimates for α-harmonic measure.

Heat kernel of fractional Laplacian in cones

Krzysztof Bogdan, Tomasz Grzywny (2010)

Colloquium Mathematicae

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We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.

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...

Potential spaces on fractals

Jiaxin Hu, Martina Zähle (2005)

Studia Mathematica

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We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered.