University of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601Essential Norm of the Generalized Integration Operator from Zygmund Space into Weighted Dirichlet Type Space334725196610.22130/scma.2022.521137.888ENFaribaAlighadrDepartment of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.HamidVaeziDepartment of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.MostafaHassanlooEngineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran.Journal Article20201214Let $H(\mathbb{D})$ 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<br />$$I_{g,\varphi}^{(n)}(f)(z)=\int_0^z f^{(n)}(\varphi(\xi))g(\xi)\ d\xi,\quad z\in\mathbb{D},$$ 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.https://scma.maragheh.ac.ir/article_251966_ddba7c527ec8fcace5d324b22d964021.pdf