Wolff's Ideal Theorem on Qp Spaces

TL;DR

This paper extends Wolff's Ideal Theorem from bounded analytic functions to the intersection of bounded functions with Qp spaces and their multiplier algebras, broadening its applicability in complex analysis.

Contribution

The paper proves the extension of Wolff's Ideal Theorem to the Banach algebra $H^{ abla}( abla)$ intersected with Qp spaces and to their multiplier algebras, which was previously unestablished.

Findings

Wolff's Ideal Theorem is valid on $H^{ abla}( abla) igcap Q_p$ spaces.

The theorem also extends to the multiplier algebra on $Q_p$ spaces.

This broadens the scope of ideal theory in complex function spaces.

Abstract

For $p\in(0,1),$ let $Q_p$ spaces be the space of all analytic functions on the unit disk $\mathbb{D}$ such that $|f'(z) | ^2 (1-| z| ^2)^p dA(z)$ is a $p$ - Carleson measure. In this paper, we prove that the Wolff's Ideal Theorem on $H^\infty{(\mathbb{D})}$ can be extended to the Banach algebra $H^{\infty}(\mathbb{D})\cap Q_{p}$, and also to the multiplier algebra on $Q_p$ spaces.