Some more generalized integration operators on general function spaces

Let $H(\mathbb{D})$ be the class of all analytic functions on $\mathbb{D}$ and $\overrightarrow{h}=(h_0,h_1,\dots ,h_{n-1})$ with $h_k\in H(\mathbb{D})$ for $k=0,1,\dots ,n-1$. In this paper, we study a complex integration operator

$$\begin{array}{r}(T_{\overrightarrow{h}}^{(n)}f)(z)=I^n(h_0^{(n)}f+h_1^{(n-1)}{f}^{\prime }+\cdots +h_{n-1}^{\prime }{f}^{(n-1)})(z),f\in H(\mathbb{D}),\end{array}$$

where $I$ is the classical integration operator

$$(If)(z)={\int }_0^{z}f(w)dw$$

and $I^n$ is the $n$th iteration of $I$. We characterize the bounded and compact operators $T_{\overrightarrow{h}}^{(n)}$ on $F(p,q,s)$ by using some characterizations of the space.