Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

Krzysztof Bogdan; Paweł Sztonyk

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Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

Krzysztof Bogdan·Paweł Sztonyk

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Abstract

We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.

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Krzysztof Bogdan, Paweł Sztonyk. 2005-07-27. Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian. https://arxiv.org/abs/math/0507579

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