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

Abstract

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