Weighted composition operators on spaces of functions with derivative in a Hardy space

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 o phi) is called a weighted composition operator. For each 1 less than or equal to p less than or equal to infinity, let S-p be the space of analytic functions on D whose derivatives belong to the Hardy space H-p. In this paper we deal with boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from S-p into S-q for 1 less than or equal to p, q less than or equal to infinity.