Wolff's Problem of Ideals in the Multipler Algebra on Weighted Dirichlet Space

TL;DR

This paper extends Wolff's theorem on ideals from bounded analytic functions to the multiplier algebra of weighted Dirichlet spaces, providing new insights into the structure of these function spaces.

Contribution

It establishes an analogue of Wolff's theorem for the multiplier algebra of weighted Dirichlet spaces, a novel extension of classical ideal theory.

Findings

Proved an analogue of Wolff's theorem for weighted Dirichlet spaces.

Characterized the structure of ideals in the multiplier algebra.

Extended classical results to a broader class of function spaces.

Abstract

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