Weighted Composition Operators between Different Hardy Spaces

Let (phi) and (psi) be two analytic functions defined on D such that (phi)(D) (subset of or equal to) D. The operator given by f – (psi) (f (ring operator) (phi)) is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from a Hardy space Hp into another Hardy space Hq (1 <= p, q <= (infinity)) . We apply these results to study composition operators on Hardy spaces of a half-plane.