no. 4
Jensen measures and unbounded B-regular domains in C n
[Mesures de Jensen et domaines B-réguliers non bornés dans C n ]
Nguyen, Quang Dieu1, 2 ; Hung, Dau Hoang3
1 Current address: Seaoul National Universiy Department of Mathematics 151-742 Seoul (Korea)
2 University of Education (Dai Hoc Su Pham Hanoi) Department of Mathematics 136 Xuan Thuy, Cau Giay Hanoi (Vietnam)
3 Vinh University Department of Mathematics Vinh (Vietnam)
Annales de l'Institut Fourier, Tome 58 (2008) no. 4, pp. 1383-1406.

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

DOI : 10.5802/aif.2388
Classification : 32T27
Keywords: Plurisubharmonic function, Dirichlet-Bremermann problem, $B$-regular domain
Mot clés : fonction plurisousharmonique, Dirichlet-Bremermann problème, domaine $B$-régulier

Nguyen, Quang Dieu 1, 2 ; Hung, Dau Hoang 3

1 Current address: Seaoul National Universiy Department of Mathematics 151-742 Seoul (Korea)
2 University of Education (Dai Hoc Su Pham Hanoi) Department of Mathematics 136 Xuan Thuy, Cau Giay Hanoi (Vietnam)
3 Vinh University Department of Mathematics Vinh (Vietnam) 
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Nguyen, Quang Dieu; Hung, Dau Hoang. Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$. Annales de l'Institut Fourier, Tome 58 (2008) no. 4, pp. 1383-1406. doi : 10.5802/aif.2388. https://aif.centre-mersenne.org/articles/10.5802/aif.2388/

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