A class of operator related weighted composition operators between Zygmund space

	A class of operator related weighted composition operators between Zygmund space
AUT Journal of Mathematics and Computing
مقاله 3، دوره 2، شماره 1، اردیبهشت 2021، صفحه 17-25 اصل مقاله (335.13 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2020.18833.1041
نویسنده
Ebrahim Abbasi^*
aDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
چکیده
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.
کلیدواژه‌ها
B‎oundedness؛ Compactness؛ Essential ‎norm؛ ‎Zygmund ‎space‎
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