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

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 -