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

[Mesures de Jensen et domaines $B$-réguliers non bornés dans ${\mathbf{C}}^n$]

Nguyen, Quang Dieu ; Hung, Dau Hoang

Annales de l'Institut Fourier, Tome 58 (2008), p. 1383-1406 / Harvested from Numdam

Résumé

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.

Abstract

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

Détail

Publié le : 2008-01-01

MR 2427964 | Zbl 1156.32020

DOI : https://doi.org/10.5802/aif.2388
Classification:  32T27
Mots clés: fonction plurisousharmonique, Dirichlet-Bremermann problème, domaine $B$-régulier

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