Generalized Volterra-type operators from Hardy space into iterated weighted-type spaces
Keywords:
Boundedness, Compactness, Generalized Volterra-type operators, Hardy space, Iterated weighted-type spacesAbstract
Let $H(\mathbb{D})$ be the set of analytic functions on {$\DD$} and for $1\leq p\leq \infty$, $H^p$ be the Hardy space.
For $m\in\mathbb{N}$ suppose that $I^m$ be {$m$}th iteration and $\overrightarrow{g}=(g_0,\cdots,g_{m-1})$ where $I(f)=\int_{0}^{z} f(w)dw$ and $\{g_i\}_{i=0}^{m-1}\subset H(\DD)$.
The generalized Volterra-type operators $I^m_{\overrightarrow{g}}$ on
$H(\DD)$ is defined as follows
$$I^m_{\overrightarrow{g}}(f)=I^m(\sum_{i=0}^{m-1}f^{(i)}g_i).$$
In this paper, we investigate boundedness and compactness {of} generalized Volterra-type operators from Hardy space into iterated weighted-type spaces,
$V_n=\{f\in H(\DD): \ \ \sup_{z\in\DD}(1-|z|^2)|f^{(n)}(z)|<\infty \}$.
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