Généralisation à $\mathbb C^n$ d'un théorème de M. Jarnicki sur les cellules d'harmonicité

Abstract

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 $n=1.$