Wolff's Problem of Ideals in the Multiplier Algebra on Dirichlet space

TL;DR

This paper extends Wolff's theorem, originally for bounded analytic functions, to the setting of the multiplier algebra on Dirichlet space, providing new insights into ideal structure in this context.

Contribution

It establishes an analogue of Wolff's theorem for the multiplier algebra of Dirichlet space, a significant extension of classical results.

Findings

Proves an analogue of Wolff's theorem for Dirichlet space multiplier algebra

Provides new understanding of ideal structure in Dirichlet space

Extends classical function theory results to a new functional setting

Abstract

We establish an analogue of Wolff's theorem on ideals in $H^{\infty}(\mathbb{D})$ for the multiplier algebra of Dirichlet space.