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 $|f^{\prime }(z){|}^2(1-|z{|}^2{)}^{p}dA(z)$ 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.

Some typos have been fixed. to appear in RMJM