Forelli–Rudin estimates, Carleson measures and F(p,q,s)-functions

A classical theorem of L. Carleson states that the injection map from the Hardy space Hp into Lp(dμ) is bounded if and only if the positive measure μ on the unit disc is a bounded Carleson measure. In this paper Forelli–Rudin estimates for arbitrary positive measures on the unit disc are proved, and then these estimates are applied to characterize bounded s-Carleson measures in terms of α-Bloch- and F(p,q,s)-functions.