Products of redial derivative and integral-type operators from Zygmund spaces to Bloch spaces

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 $$I_{\varphi }^{g}f(z)={\int }_0^1\Re f(\varphi (tz))g(tz)\frac{dt}{t},z\in \mathbb{B}$$ where $g\in H(\mathbb{B}),g(0)=0$, $\varphi$ is a holomorphic self-map of $\mathbb{B}$,\ between Zygmund spaces and Bloch spaces.

arXiv comment13 pages