Regular Article
Weighted Composition Operators on Hardy Spaces,☆☆

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Abstract

Let ϕ, ψ be analytic functions defined on D, such that ϕ(D)  D. The operator given by f  ψ(f  ϕ) is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators on Hardy spaces Hp (1  p < ∞). In particular, we prove that such an operator is compact on H1 if and only if it is 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.

Keywords

weighted composition operators
Hardy spaces
compact operators
weakly compact operators
completely continuous operators

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This research has been partially supported by DGESIC project PB97-0706 and by La Consejerı́a de Educación y Ciencia de la Junta de Andalucı́a.

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Submitted by William, F. Ames