Generalized weighted composition operators from area Nevanlinna spaces to weighted-type spaces
Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1195-1205
Printed November 1, 2011
Yang Weifeng and Yan Weiren
Hunan Institute of Engineering, Hunan Institute of Engineering
Abstract : Let $H(\mathbb D)$ denote the class of all analytic functions on the open unit disk $\mathbb D$ of the complex plane $\mathbb C $. Let $n$ be a nonnegative integer, $\varphi$ be an analytic self-map of $\mathbb D$ and $u\in H(\mathbb D)$. The generalized weighted composition operator is defined by $$ D^n_{\varphi,u}f=uf^{(n)}\circ \varphi,~~ f\in H(\mathbb D). $$ The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.
Keywords : generalized weighted composition operator, area Nevanlinna space, weighted-type space
MSC numbers : Primary 47B38; Secondary 30H05
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