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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)

MSC:
47B33Composition operators
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References:
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