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Weighted Composition Operators on Hardy Spaces

✍ Scribed by Manuel D Contreras; Alfredo G Hernández-Dı́az

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
94 KB
Volume
263
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let

, be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ž . given by f ¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ž . ity of weighted composition operators on Hardy spaces H 1 F p -ϱ . In p particular, we prove that such an operator is compact on H if and only if it is 1 weakly compact on this space. This result depends on a technique which passes the weak compactness from an operator T to operators dominated in norm by T.

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