%0 Journal Article
%T A class of operator related weighted composition operators between Zygmund space
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Abbasi, Ebrahim
%D 2021
%\ 02/01/2021
%V 2
%N 1
%P 17-25
%! A class of operator related weighted composition operators between Zygmund space
%K Boundedness
%K Compactness
%K essential norm
%K Zygmund space
%R 10.22060/ajmc.2020.18833.1041
%X 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\begin{align*}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}.\end{align*}In this work, we obtain some new characterizations for boundedness and essential norm of operator $T_{u, v, \varphi}$ between Zygmund space.
%U https://ajmc.aut.ac.ir/article_4132_108bb500418e96e24d8b8076a85ae3b0.pdf