[Sous-extension des fonctions plurisousharmoniques de masse de Monge–Ampère bornée]
Soit
On démontre alors que pour tout domaine hyperconvexe
Let
It is known that the complex Monge–Ampère operator is well defined on the class
We prove that if
From this result we deduce a global uniform integrability theorem for the classes of plurisubharmonic functions with uniformly bounded Monge–Ampère masses on
Accepté le :
Publié le :
Urban Cegrell 1 ; Ahmed Zeriahi 2
@article{CRMATH_2003__336_4_305_0, author = {Urban Cegrell and Ahmed Zeriahi}, title = {Subextension of plurisubharmonic functions with bounded {Monge{\textendash}Amp\`ere} mass}, journal = {Comptes Rendus. Math\'ematique}, pages = {305--308}, publisher = {Elsevier}, volume = {336}, number = {4}, year = {2003}, doi = {10.1016/S1631-073X(03)00031-1}, language = {en}, }
Urban Cegrell; Ahmed Zeriahi. Subextension of plurisubharmonic functions with bounded Monge–Ampère mass. Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 305-308. doi : 10.1016/S1631-073X(03)00031-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00031-1/
[1] Domains of existence for plurisubharmonic functions, Math. Ann., Volume 238 (1978) no. 1, pp. 67-69
[2] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1981), pp. 1-40
[3] Smooth plurisubharmonic functions without subextension, Math. Z., Volume 198 (1988) no. 3, pp. 331-337
[4] On the domains of existence for plurisubharmonic functions, Complex Analysis, Warsaw, 1979, Banach Center Publ., 11, PWN, Warsaw, 1983, pp. 33-37
[5] Pluricomplex energy, Acta Math., Volume 180 (1998), pp. 187-217
[6] U. Cegrell, The general definition of the complex Monge–Ampère operator, Preprint of Umeå University and Mid Sweden University, 2002
[7] Fonctions plurisousharmoniques et ensembles pluripolaires, Séminaire Lelong–Skoda, Lecture Notes in Math., 822, Springer-Verlag, 1980, pp. 61-76
[8] Plurisubharmonic functions on ring domains, Complex Analysis, Univ. Park, 1986, Lecture Notes in Math., 1268, Springer-Verlag, 1987, pp. 111-120
[9] The range of the complex Monge–Ampère operator, Indiana Univ. Math. J., Volume 44 (1995) no. 3, pp. 765-783
[10] The complex Monge–Ampère equation, Acta Math., Volume 180 (1998), pp. 69-117
[11] Pluricomplex Green functions and the Dirichlet problem for complex Monge–Ampère operator, Michigan Math. J., Volume 44 (1997), pp. 579-596
[12] Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions, Indiana Univ. Math. J., Volume 50 (2001) no. 1, pp. 671-703
[13] A. Zeriahi, Local uniform integrability and the size of plurisubharmonic lemniscates in terms of Hausdorff–Riesz measures, Prépublication n° 222, Laboratoire Emile Picard, UPS-Toulouse, 2001
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