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

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 $$I_{g,varphi}^{(n)}(f)(z)=int_0^z f^{(n)}(varphi(xi))g(xi) dxi,quad zinmathbb{D},$$ from Zygmund space into weighted Dirichlet type space, where $varphi$ is an analytic self-map of $mathbb{D}$, $ninmathbb{N}$ and $gin H(mathbb{D})$. Also we give an estimate for the essential norm of the above operator.