A ‎c‎lass of operator ‎r‎‎elated weighted composition operators ‎between‎ Zygmund ‎s‎‎pace‎

Document Type : Original Article

Author

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

10.22060/ajmc.2020.18833.1041

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 $u‎, ‎vin H(mathbb{D})$ 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 fin H(mathbb{D} )‎, ‎quad zin 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.

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Main Subjects


Volume 2, Issue 1
Winter and Spring 2021
Pages 17-25
  • Receive Date: 06 August 2020
  • Revise Date: 25 September 2020
  • Accept Date: 25 September 2020