Atomic decomposition for Bergman spaces with exponential type weights

TL;DR

This paper demonstrates that functions in Bergman spaces with exponential weights can be represented as infinite series of kernel functions, providing a new way to analyze such spaces.

Contribution

It introduces an atomic decomposition method for Bergman spaces with exponential weights, enabling new analytical techniques.

Findings

Functions in these spaces admit atomic decompositions.

The series representation converges in the space topology.

This approach generalizes previous results for polynomial weights.

Abstract

We show that any function in a Bergman space with exponential type weights admits a representation in terms of an infinite series of kernel functions.