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

TL;DR

This paper establishes upper pointwise estimates for the Bergman kernel of weighted Bergman spaces with exponential type weights on the unit disk, advancing understanding of kernel behavior under specific subharmonic weight conditions.

Contribution

It provides new upper pointwise estimates for the Bergman kernel in weighted spaces with exponential weights, under certain subharmonic function conditions.

Findings

Derived upper pointwise estimates for the Bergman kernel

Applicable to weights given by subharmonic functions

Enhances understanding of kernel behavior in weighted spaces

Abstract

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