In this paper, it is proved that if $f:D\rightarrow D^{\prime }
$ is a holomorphic homeomorphism between two domains $D$
and $D^{\prime }$ in $\CC^n(n\geq 2)$
which commutes with the Lelong transformation $T,$ then $f$
extends to a holomorphic homeomorphism $\widetilde{f}$
between the corresponding cells of harmonicity ${\cal H}(D)$ and
${\cal H}(D^{\prime }).$ In such way a generalization is given
of Jarnicki 's result obtained in the case $n=1.$
Publié le : 2004-09-14
Classification:
Cellule d'harmonicité,
Transformation de Lelong,
Chemin de Lelong,
Extension holomorphe de Jarnicki,
32A30,
31A30,
31B30
@article{1093351378,
author = {Boutaleb, M.},
title = {G\'en\'eralisation \`a $\mathbb C^n$ d'un th\'eor\`eme de M.
Jarnicki sur les cellules d'harmonicit\'e},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 365-373},
language = {fr},
url = {http://dml.mathdoc.fr/item/1093351378}
}
Boutaleb, M. Généralisation à $\mathbb C^n$ d'un théorème de M.
Jarnicki sur les cellules d'harmonicité. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 365-373. http://gdmltest.u-ga.fr/item/1093351378/