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

Contreras, Manuel D.; Hernández-Díaz, Alfredo G.

J. Math. Anal. Appl. 263, No. 1, 224-233 (2001).

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:

47B33

Linear composition operators

Keywords:

Hardy space; composition operator; boundedness; compactness; weak compactness; complete continuity

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