Wolff's ideal theorem on $Q_p$ spaces

Abstract

For $p\in (0,1)$, let $Q_p$ space be the space of all analytic functions on the unit disk $\mathbb {D}$ such that $\vert f'(z) \vert ^2 (1-\vert z\vert ^2)^p\, dA(z)$ is a $p$-Carleson measure. We prove that 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.