Fariba Alighadr - Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
Hamid Vaezi - Department of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Mostafa Hassanloo - Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran.

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 operatorI_{g,\varphi}^{(n)}(f)(z)=\int_۰^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.

Generalized integration operator, Dirichlet type space, Zygmund space, Essential norm