Wolff's Ideal Theorem on Qp 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.