Closed ideals in some algebras of analytic functions

TL;DR

This paper characterizes all closed ideals within a specific algebra of analytic functions combining Dirichlet and Lipschitz conditions, advancing understanding of their algebraic structure.

Contribution

It provides a complete description of closed ideals in the algebra formed by the intersection of Dirichlet space and Lipschitz class for 0<α≤1/2.

Findings

Complete characterization of closed ideals

Describes algebraic structure of the intersection space

Advances understanding of analytic function algebras

Abstract

We obtain a complete description of closed ideals of the algebra $\mathcal{D}\cap \mathrm{lip}_\alpha},$ $0<\alpha\leq{1/2},$ where $\mathcal{D}$ is the Dirichlet space and $\mathrm{lip}_\alpha}$ is the algebra of analytic functions satisfying the Lipschitz condition of order $\alpha.$