WEIGHTED COMPOSITION OPERATORS ON SPACES OF FUNCTIONS WITH DERIVATIVE IN A HARDY SPACE

Let φ and ψ be two analytic functions defined on D such that φ(D) ⊆ D. The operator given by f ↦ ψ(f ○ φ) is called a weighted composition operator. For each 1 ≤ p ≤ ∞, let Sp be the space of analytic functions on D whose derivatives belong to the Hardy space Hp. In this paper we deal with boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from Sp into Sq for 1 ≤ p, q ≤ ∞.