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 H-P into L-P(d mu) is bounded if and only if the positive measure mu 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 alpha-Bloch- and F(p, q, s)-functions. (c) 2005 Elsevier Inc. All rights reserved.