@Article{Hu2016,
author="Qinghua Hu, Xiangling Zhu",
title="Essential norm of weighted composition operators from \(H^\infty\) to the Zygmund space",
year="2016",
volume="9",
number="7",
pages="5082--5092",
abstract="Let \(\varphi\) be an analytic self-map of the unit disk \(\mathbb{D}\) and \(u \in H(\mathbb{D})\), the space of analytic functions on \(\mathbb{D}\). The
weighted composition operator, denoted by \(uC_\varphi\), is defined by \((uC_\varphi f)(z) = u(z)f(\varphi(z)); f \in H(\mathbb{D}); z \in \mathbb{D}.\)
In this paper, we give three different estimates for the essential norm of the operator \(uC_\varphi\) from \(H^\infty\) into the
Zygmund space, denoted by \(\mathcal{Z}\). In particular, we show that\(\|uC_\varphi\|_{e,H^\infty\rightarrow \mathcal{Z}} \approx \limsup_{n\rightarrow\infty}\|u\varphi^n\|_\mathcal{Z}\).",
issn="ISSN 2008-1901",
doi="10.22436/jnsa.009.07.11",
url="http://dx.doi.org/10.22436/jnsa.009.07.11"
}