GENERALIZED INTEGRATION OPERATORS BETWEEN BLOCH-TYPE SPACES AND $F(p,q,s)$ SPACES

Abstract

Let $H(\mathbb{D})$ denote the space of all holomorphic functions on the unit disk $\mathbb{D}$ of $\mathbb{C}$. Let $\varphi$ be a holomorphic self-map of $\mathbb{D}$, $n$ be a positive integer and $g\in H(\mathbb{D})$. In this paper, we investigate the boundedness and compactness of a generalized integration operator $$ I^{(n)}_{g,\varphi}f(z) = \int^z_0 f^{(n)}(\varphi(\zeta)) g(\zeta) d\zeta,\ \ z \in \mathbb{D},$$ between Bloch-type spaces and $F(p,q,s)$ spaces.