Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$

Nguyen, Quang Dieu; Hung, Dau Hoang

Annales de l'Institut Fourier, Tome 58 (2008) no. 4, pp. 1383-1406

Following Sibony, we say that a bounded domain $\Omega$ in $C^n$ is $B$-regular if every continuous real valued function on the boundary of $\Omega$ can be extended continuously to a plurisubharmonic function on $\Omega$. The aim of this paper is to study an analogue of this concept in the category of unbounded domains in $C^n$. The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

En suivant Sibony, nous dirons qu’un domaine borne $\Omega$ de $C^n$ est $B-$ régulier si toute fonction continue à valeurs réelles sur la frontière de $\Omega$ peut être prolongée continûment à une fonction plurisousharmonique sur $\Omega$. Le but de ce papier est d’étudier une notion analogue dans la catégorie des domaines non bornés dans $C^n$. L’usage des mesures de Jensen relatives à des classes de fonctions plurisousharmoniques jouent un rôle clé dans notre travail.

Classification : 32T27
Keywords: Plurisubharmonic function, Dirichlet-Bremermann problem, $B$-regular domain
Mots-clés : fonction plurisousharmonique, Dirichlet-Bremermann problème, domaine $B$-régulier

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