Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights

Saïd Asserda; Amal Hichame

doi:10.1016/j.crma.2013.11.001

Complex analysis

Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights

Presented by: Jean-Pierre Demailly

Saïd Asserda ¹; Amal Hichame ²

¹ Ibn Tofail University, Faculty of Sciences, Department of Mathematics, PO 242 Kenitra, Morocco
² Regional Centre of Trades of Education and Training, Kenitra, Morocco

Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 13-16.

Abstract
Résumé

Let ${AL}_{ϕ}^{2} (D)$ denote the closed subspace of $L^{2} (D, e^{- 2 ϕ} d λ)$ consisting of holomorphic functions in the unit disc $D$ . For certain class of subharmonic functions $ϕ : D \to D$ , we prove an upper pointwise estimate for the Bergman kernel for ${AL}_{ϕ}^{2} (D)$ .

Soit ${AL}_{ϕ}^{2} (D)$ le sous-espace fermé de $L^{2} (D, e^{- 2 ϕ} d λ)$ formé des fonctions holomorphes sur le disque unité $D$ . Pour une classe de fonctions sous-harmoniques $ϕ : D \to D$ , on établit une estimation ponctuelle du noyau de Bergman de ${AL}_{ϕ}^{2} (D)$ .

Received: 2013-09-19
Accepted: 2013-11-04
Published online: 2013-12-17

DOI: 10.1016/j.crma.2013.11.001

Author's affiliations:

Saïd Asserda ¹; Amal Hichame ²

¹ Ibn Tofail University, Faculty of Sciences, Department of Mathematics, PO 242 Kenitra, Morocco
² Regional Centre of Trades of Education and Training, Kenitra, Morocco

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     author = {Sa{\"\i}d Asserda and Amal Hichame},
     title = {Pointwise estimate for the {Bergman} kernel of the weighted {Bergman} spaces with exponential type weights},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {13--16},
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     number = {1},
     year = {2014},
     doi = {10.1016/j.crma.2013.11.001},
     language = {en},
}

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Saïd Asserda; Amal Hichame. Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 13-16. doi : 10.1016/j.crma.2013.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.001/

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