Nguyen, Quang Dieu; Hung, Dau Hoang
Jensen measures and unbounded B-regular domains in C n  [ Mesures de Jensen et domaines B-réguliers non bornés dans C n  ]
Annales de l'institut Fourier, Tome 58 (2008) no. 4 , p. 1383-1406
MR 2427964 | Zbl 1156.32020
doi : 10.5802/aif.2388
URL stable : http://www.numdam.org/item?id=AIF_2008__58_4_1383_0

Classification:  32T27
Mots clés: fonction plurisousharmonique, Dirichlet-Bremermann problème, domaine B-régulier
En suivant Sibony, nous dirons qu’un domaine borne Ω de C n est B- régulier si toute fonction continue à valeurs réelles sur la frontière de Ω peut être prolongée continûment à une fonction plurisousharmonique sur Ω. 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.
Following Sibony, we say that a bounded domain Ω in C n is B-regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω. 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

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