Closed ideals in analytic weighted Lipschitz algebras

TL;DR

This paper characterizes all closed ideals in a class of weighted Lipschitz algebras of analytic functions on the unit disk, defined by a specific modulus of continuity condition.

Contribution

It provides a complete description of closed ideals in weighted Lipschitz algebras with a given modulus of continuity, extending understanding of their structure.

Findings

Complete characterization of closed ideals in weighted Lipschitz algebras

Identification of conditions on the modulus of continuity for ideal structure

Extension of classical results to weighted analytic function spaces

Abstract

We obtain a complete description of closed ideals in weighted Lipschitz algebras $\Lambda_\omega$ of analytic functions on the unit disk satisfying the following condition $$\frac{|f(z)-f(w)|}{\omega(|z-w|)}=o(1)\qquad(as |z-w| \longrightarrow 0),$$ where $\omega$ is a modulus of continuity satisfying some regularity conditions.