Volume 35 • Number 3 • 2012   • An Integral-Type Operator from $H^\infty$ to Zygmund-Type Spaces Xiangling Zhu Abstract. Let $g \in H(\mathbb{D})$, $n$ be a nonnegative integer and $\varphi$ be an analytic self-map of $\mathbb{D}$. We study the boundedness and compactness of the integral operator $C^n_{\varphi,g} $ defined by \begin{align} (C^n_{\varphi,g} f)(z)=\int_0^z f^{(n)} ( \varphi(\xi) )g(\xi) d\xi, \quad z\in \mathbb D, \ f\in H(\mathbb D),\nonumber \end{align} from $H^\infty$ to Zygmund-type spaces on the unit disk. 2010 Mathematics Subject Classification: Primary: 47B38; Secondary: 30H05. Full text: PDF