Cyclicity of singular inner functions from the corona theorem

TL;DR

This paper applies Carleson's corona theorem to establish new results on the cyclicity of singular inner functions in weighted Bergman spaces, notably without requiring regularity conditions on the weights.

Contribution

It introduces a novel approach using the corona theorem to analyze cyclicity without regularity assumptions on weights.

Findings

Established cyclicity results for singular inner functions in weighted Bergman spaces.

Developed a method that avoids regularity conditions on weights.

Extended understanding of function cyclicity in complex analysis.

Abstract

Carleson's corona theorem is used to obtain two results on cyclicity of singular inner functions in weighted Bergman-type spaces on the unit disk. Our method proof requires no regularity conditions on the weights.