We investigate the Green function, the Poisson kernel and the Martin kernel of circular cones in the symmetric stable case. We derive their sharp estimates. We also investigate properties of the characteristic exponent of these estimates. We prove that this exponent is a continuous function of the aperture of the cone.
Publié le : 2006-03-14
Classification:
Stable process,
𝛼-harmonic function,
Green function,
Poisson kernel,
Martin kernel,
circular cone,
31B25,
60J45
@article{1147883392,
author = {Michalik, Krzysztof},
title = {Sharp estimates of the Green function, the Poisson kernel and the Martin kernel of cones for symmetric stable processes},
journal = {Hiroshima Math. J.},
volume = {36},
number = {1},
year = {2006},
pages = { 1-21},
language = {en},
url = {http://dml.mathdoc.fr/item/1147883392}
}
Michalik, Krzysztof. Sharp estimates of the Green function, the Poisson kernel and the Martin kernel of cones for symmetric stable processes. Hiroshima Math. J., Tome 36 (2006) no. 1, pp. 1-21. http://gdmltest.u-ga.fr/item/1147883392/