Weighted inequalities involving Hardy and Copson operators

Abstract

We characterize a four-weight inequality involving the Hardy operator and the Copson operator. More precisely, given p1, p2, q1, q2 ∈ (0, ∞), we find necessary and sufficient conditions on nonnegative measurable functions u1, u2, v1, v2 on (0, ∞) for which there exists a positive constant c such that the inequalityand classical Lorentz spaces of type Λ.2000 Mathematics Subject Classification. 26D10, 46E20.