PRODUCTS OF MULTIPLICATION, COMPOSITION AND DIFFERENTIATION OPERATORS FROM MIXED-NORM SPACES TO WEIGHTED-TYPE SPACES

Abstract

Let $\varphi$ be an analytic self-map of the unit disk $\mathbb{D}$, $H(\mathbb{D})$ the space of analytic functions on $\mathbb{D}$ and $\psi_{1},\psi_{2}\in H(\mathbb{D})$. Recently Stevi$\acute{\hbox{c}}$ and co-workers defined the following operator $$T_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_{1}(z)f(\varphi(z))+\psi_{2}(z)f'(\varphi(z)),\ \ \ f\in H(\mathbb{D}).$$ The boundedness and compactness of the operators $T_{\psi_{1},\psi_{2},\varphi}$ from mixed-norm spaces to weighted-type spaces are investigated in this paper.