The general definition of the complex Monge-Ampère operator
Annales de l'Institut Fourier, Volume 54 (2004) no. 1, p. 159-179

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.

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.

DOI : https://doi.org/10.5802/aif.2014
Classification:  32U15,  32W20
Keywords: complex Monge-Ampère operator, plurisubharmonic function
@article{AIF_2004__54_1_159_0,
     author = {Cegrell, Urban},
     title = {The general definition of the complex Monge-Amp\`ere operator},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {1},
     year = {2004},
     pages = {159-179},
     doi = {10.5802/aif.2014},
     zbl = {1065.32020},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_1_159_0}
}
The general definition of the complex Monge-Ampère operator. Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 159-179. doi : 10.5802/aif.2014. http://www.numdam.org/item/AIF_2004__54_1_159_0/

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