On an Extension of Stević–Sharma Operator from Weighted Bergman–Orlicz Space to Weighted-Type Space on the Unit Ball

Abstract

Let $H({{\mathbb {B}}})$ denote the space of holomorphic functions on the unit ball ${{\mathbb {B}}}$ of ${{\mathbb {C}}}^{n}$, $\psi _{1}, \psi _{2}, \psi _{3}\in H({{\mathbb {B}}})$ and $\varphi$ be a holomorphic self-map of ${{\mathbb {B}}}$. In this paper, we are devoted to investigating the metrical boundedness and metrical compactness of the following extension of Stević–Sharma operator that proposed by Liu and Yu

$$\begin{aligned} T_{\psi _{1},\psi _{2},\psi _{3},\varphi }f(z)=\psi _{1}(z)f(\varphi (z))+\psi _{2}(z){{\mathcal {R}}}f(\varphi (z)) +\psi _{3}(z){{\mathcal {R}}}(f\circ \varphi )(z),\quad z\in {{\mathbb {B}}}, \end{aligned}$$

where ${{\mathcal {R}}}$ is the radial derivative operator, from the weighted Bergman–Orlicz space $A_{\alpha }^{\Phi }({{\mathbb {B}}})$ to weighted-type space $H_{\mu }^{\infty }({{\mathbb {B}}})$ (or $H_{\mu ,0}^{\infty }({{\mathbb {B}}})$) under a condition that introduced by Wang et al.