Wolff's Ideal Theorem on Qp Spaces

For $p\in (0,1),$ let $Q_p$ spaces be the space of all analytic functions on the unit disk $\mathbb{D}$ such that $\mathrm{\mid }{f}^{\mathrm{\prime }}(z){\mathrm{\mid }}^2(1-\mathrm{\mid }z{\mathrm{\mid }}^2{)}^{p}dA(z)$ is a $p$

• Carleson measure. In this paper, we prove that the Wolff’s Ideal Theorem on $H^{\mathrm{\infty }}(\mathbb{D})$ can be extended to the Banach algebra $H^{\mathrm{\infty }}(\mathbb{D})\cap Q_p$, and also to the multiplier algebra on $Q_p$ spaces.