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

Krzysztof Bogdan; Paweł Sztonyk

Studia Mathematica (2007)

  • Volume: 181, Issue: 2, page 101-123
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Krzysztof Bogdan, and Paweł Sztonyk. "Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian." Studia Mathematica 181.2 (2007): 101-123. <http://eudml.org/doc/284988>.

@article{KrzysztofBogdan2007,
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.},
author = {Krzysztof Bogdan, Paweł Sztonyk},
journal = {Studia Mathematica},
keywords = {potential kernel; Harnack's inequality; relative Kato condition; Green function; stable process},
language = {eng},
number = {2},
pages = {101-123},
title = {Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian},
url = {http://eudml.org/doc/284988},
volume = {181},
year = {2007},
}

TY - JOUR
AU - Krzysztof Bogdan
AU - Paweł Sztonyk
TI - Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 2
SP - 101
EP - 123
AB - 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.
LA - eng
KW - potential kernel; Harnack's inequality; relative Kato condition; Green function; stable process
UR - http://eudml.org/doc/284988
ER -

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