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Weighted composition operators on some weighted spaces in the unit ball. (English) Zbl 1160.47024

For a positive weight function \(\mu\) on \([0,1)\), the space \(H^\infty_\mu\) consists of analytic functions \(f\) in the unit disc \(D\) such that \[ \sup_{z\in D}\mu(| z| )| f(z)| <\infty. \] The paper studies weighted composition operators \(uC_\varphi\) on the spaces \(H^\infty_\mu\), where \(u\) is an analytic function in \(D\) and \(\varphi\) is an analytic self-map of \(D\). The main problems studied include the boundedness and compactness of these operators on various \(H^\infty_\mu\) spaces.
Reviewer: Kehe Zhu (Albany)

MSC:

47B33 Linear composition operators
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