Weighted composition operators on Hardy spaces. (English) Zbl 1026.47016

This paper studies operators of the form \(f\mapsto (f\circ\varphi)\psi\) acting on Hardy spaces \(H^p\) of the unit disk \(D\), where \(\psi\) is analytic in \(D\) and \(\varphi\) is an analytic self-map of \(D\). Problems studied include the boundedness, compactness, weak compactness, and complete continuity of such operators. In particular, it is shown that such an operator is compact on \(H^1\) if and only if it is weakly compact on \(H^1\).
Reviewer: K.Zhu (Albany)


47B33 Linear composition operators
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