Products of redial derivative and integral-type operators from Zygmund spaces to Bloch spaces (1111.5126v1)

Abstract: Let $H(\mathbb{B})$ denote the space of all holomorphic functions on the unit ball $\mathbb{B}\in \mathbb{C}^n$. In this paper we investigate the boundedness and compactness of the products of radial derivative operator and the following integral-type operator $$ I_\phi^g f(z)=\int_0^1 \Re f(\phi(tz))g(tz)\frac{dt}{t},\ z\in\mathbb{B} $$ where $g\in H(\mathbb{B}), g(0)=0$, $\phi$ is a holomorphic self-map of $\mathbb{B}$,\ between Zygmund spaces and Bloch spaces.