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

Asserda, Saïd; Hichame, Amal

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

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

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

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