A class of operator related weighted composition operators between Zygmund space

Document Type : Original Article

Author

aDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran

Abstract

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.

Keywords

Main Subjects

References

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AUT Journal of Mathematics and Computing
Volume 2, Issue 1
February 2021
Pages 17-25

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