TY - JOUR
ID - 251966
TI - Essential Norm of the Generalized Integration Operator from Zygmund Space into Weighted Dirichlet Type Space
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Alighadr, Fariba
AU - Vaezi, Hamid
AU - Hassanloo, Mostafa
AD - Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
AD - Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran.
Y1 - 2022
PY - 2022
VL - 19
IS - 2
SP - 33
EP - 47
KW - Generalized integration operator
KW - Dirichlet type space
KW - Zygmund space
KW - Essential norm
DO - 10.22130/scma.2022.521137.888
N2 - Let $H(\mathbb{D})$ be the space of all analytic functions on the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$. In this paper, we investigate the boundedness and compactness of the generalized integration operator$$I_{g,\varphi}^{(n)}(f)(z)=\int_0^z f^{(n)}(\varphi(\xi))g(\xi)\ d\xi,\quad z\in\mathbb{D},$$ from Zygmund space into weighted Dirichlet type space, where $\varphi$ is an analytic self-map of $\mathbb{D}$, $n\in\mathbb{N}$ and $g\in H(\mathbb{D})$. Also we give an estimate for the essential norm of the above operator.
UR - https://scma.maragheh.ac.ir/article_251966.html
L1 - https://scma.maragheh.ac.ir/article_251966_ddba7c527ec8fcace5d324b22d964021.pdf
ER -