Weighted Composition Operators on Hardy Spaces

  title={Weighted Composition Operators on Hardy Spaces},
  author={Manuel D. Contreras and Alfredo Garc{\'i}a Hern{\'a}ndez-D{\'i}az},
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… CONTINUE READING