Complex analysis/Functional analysis
On holomorphic domination, II
[Sur la majoration holomorphe, II]

Présenté par : Jean-Pierre Demailly

Patyi, Imre1
1 Department of Mathematics, Mail Stop 561, East Carolina University, 1000 E 5th St, Greenville, NC 27858-4353, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 501-503.

Étant donnée une fonction localement bornée u:Ω→R sur un ouvert pseudoconvexe Ω dans un espace de Banach séparable jouissant de la propriété d'approximation bornée, on montre ici qu'il y a une majoration de la forme u(x)<‖h(x)‖ pour x∈Ω, où h:Ω→Z est une fonction holomorphe convenable à valeurs dans un espace de Banach convenable Z. Une majoration holomorphe comme celle ci-dessus est une propriété de convexité holomorphe qui joue un rôle profitable en analyse complexe sur des variétés de Banach.

Let X be a separable Banach space with the bounded approximation property, Ω⊂X pseudoconvex open, and u:Ω→R locally upper bounded. We show that there are a Banach space Z and a holomorphic function h:Ω→Z with u(x)<‖h(x)‖ for x∈Ω.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.04.001
Patyi, Imre 1

1 Department of Mathematics, Mail Stop 561, East Carolina University, 1000 E 5th St, Greenville, NC 27858-4353, USA 
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Patyi, Imre. On holomorphic domination, II. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 501-503. doi : 10.1016/j.crma.2015.04.001. https://www.numdam.org/articles/10.1016/j.crma.2015.04.001/

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