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Essential Norm of the Generalized Integration Operator from Zygmund Space into Weighted Dirichlet Type Space

Document Type : Research Paper

Authors

1 Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

3 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran.

Abstract

Let $H(\mathbb{D})$ be the space of all analytic functions on the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$. In this paper, we investigate the boundedness and compactness of the generalized integration operator
$$I_{g,\varphi}^{(n)}(f)(z)=\int_0^z f^{(n)}(\varphi(\xi))g(\xi)\ d\xi,\quad z\in\mathbb{D},$$ from Zygmund space into weighted Dirichlet type space, where $\varphi$ is an analytic self-map of $\mathbb{D}$, $n\in\mathbb{N}$ and $g\in H(\mathbb{D})$. Also we give an estimate for the essential norm of the above operator.

Keywords

References
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Sahand Communications in Mathematical Analysis
Volume 19, Issue 2
June 2022
Pages 33-47
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