The general definition of the complex Monge-Ampère operator
[Une définition générale de l'opérateur de Monge-Ampère complexe]
Cegrell, Urban1
1 Ume{\aa} University, Department of Mathematics, 901 87 Ume{\aa} (Suède)
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 159-179.

On définit et étudie le domaine de définition de l'opérateur de Monge-Ampère complexe. Ce domaine est le plus général possible si on impose que l'opérateur soit continu pour les limites décroissantes. Ce domaine est donné à l'aide d'approximation par certaines fonctions plurisousharmoniques jouant le rôle de "fonctions test". On démontre des estimations, on étudie un théorème de décomposition pour les mesures positives et on résout le problème de Dirichlet.

We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.

DOI : 10.5802/aif.2014
Classification : 32U15, 32W20
Keywords: complex Monge-Ampère operator, plurisubharmonic function
Mot clés : opérateur de Monge-Ampère complexe, fonction plurisousharmonique
Cegrell, Urban 1

1 Ume{\aa} University, Department of Mathematics, 901 87 Ume{\aa} (Suède) 
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Cegrell, Urban. The general definition of the complex Monge-Ampère operator. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 159-179. doi : 10.5802/aif.2014. http://www.numdam.org/articles/10.5802/aif.2014/

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