TY - JOUR
ID - 4132
TI - A class of operator related weighted composition operators between Zygmund space
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Abbasi, Ebrahim
AD - aDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 17
EP - 25
KW - Boundedness
KW - Compactness
KW - essential norm
KW - Zygmund space
DO - 10.22060/ajmc.2020.18833.1041
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4132.html
L1 - https://ajmc.aut.ac.ir/article_4132_108bb500418e96e24d8b8076a85ae3b0.pdf
ER -