On the dimension of the Bergman space for some unbounded domains

TL;DR

This paper provides a sufficient condition for the Bergman space to be infinite dimensional, applicable to pseudoconvex domains with at least one smooth boundary point of finite type.

Contribution

It introduces a new criterion linking boundary regularity to the infinite dimensionality of the Bergman space for certain unbounded domains.

Findings

Bergman space is infinite dimensional under the given condition.

The condition applies to pseudoconvex domains with smooth boundary points of finite type.

Provides a geometric criterion for the dimension of the Bergman space.

Abstract

A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of D'Angelo.