Weighted Composition Operators on Hardy Spaces1

Let , be analytic functions defined on , such that Ž . . The operator given by f Žf .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 Ž1 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.