On a Stevic Integral-Type Operator From Generally Weighted Bloch Spaces to Bloch-Type Spaces on the Unit Ball

Abstract

Let $g\in H(\mathcal{B})$, $g(0)=0$ and $\phi$ be a holomorphic self-map of the unit ball $\mathbb{B}$ in ${\mathbb{C}}^n$. The following integral-type operator

$$I_{\phi }^g(f)(z)={\int }_0^1\mathcal{R}f(\phi (tz))g(tz)\frac{dt}{t},f\in H(\mathbb{B}),z\in \mathbb{B},$$

was recently introduced by S. Stević and studied on some spaces of holomorphic functions on $\mathbb{B}$, where $\mathcal{R}f(z)=\sum _{k=1}^n{z}_k\frac{\mathrm{\partial }f}{\mathrm{\partial }{z}_k}(z)$ is the radial derivative of $g$. The boundedness and compactness of this operator from generally weighted Bloch spaces to Bloch-type spaces on $\mathbb{B}$ are investigated in this note.