Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 1 2021 02 01 A class of operator related weighted composition operators between Zygmund space 17 25 4132 10.22060/ajmc.2020.18833.1041 EN Ebrahim Abbasi aDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran Journal Article 2020 08 06 Let $\mathbb {D}$ be the open unit disk in the complex plane $\mathbb{C}$ and $H(\mathbb{D})$ be the set of all analytic functions on $\mathbb{D}$. Let $u, v\in H(\mathbb{D})$ and $\varphi$ be an analytic self-map of $\mathbb{D}$. A class of operator related weighted composition operators is defined as follow<br />\begin{align*}<br />T_{u, v, \varphi}f(z) = u(z) f{(\varphi(z))}+ v(z) f'(\varphi(z)) ,\quad f\in H(\mathbb{D} ), \quad z\in \mathbb{D}.<br />\end{align*}<br />In this work, we obtain some new characterizations for boundedness and essential norm of operator $T_{u, v, \varphi}$ between Zygmund space. https://ajmc.aut.ac.ir/article_4132_a4d8e2a7e0d0c102339f97716d2fdfb6.pdf