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

Asserda, Saïd; Hichame, Amal

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
[Estimation ponctuelle du noyau de Bergman des espaces à poids de type exponentiel]

Présenté par : Jean-Pierre Demailly

Asserda, Saïd ¹ ; Hichame, Amal 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, Tome 352 (2014) no. 1, pp. 13-16.

Résumé
Abstract

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 ${AL}_{ϕ}^{2} (D)$ .

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 ${AL}_{ϕ}^{2} (D)$ .

Reçu le : 2013-09-19
Accepté le : 2013-11-04
Publié le : 2013-12-17

DOI : 10.1016/j.crma.2013.11.001

Affiliations des auteurs :

Asserda, Saïd ¹ ; Hichame, Amal 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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Asserda, Saïd; Hichame, Amal. Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 13-16. doi : 10.1016/j.crma.2013.11.001. http://www.numdam.org/articles/10.1016/j.crma.2013.11.001/

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