Preduals of Qp -spaces II. Carleson imbeddings and atomic decompositions

Abstract

In [Aleman, A., Carlsson, M. and Persson A., Preduals of Qp -spaces. Complex Variables (To appear).], we have obtained a representation of the Cauchy-predual of the space Qp on the unit disc as a weak product of weighted Dirichlet and Bergman spaces. The present article is a continuation of Aleman et al. and contains several applications and further developments of those results. We investigate the relation between Qp and Carleson inequalities for functions in weighted Dirichlet spaces and, in particular, we prove a characterization of bounded Qp -functions in terms of pointwise multipliers between such spaces. Moreover, we use our approach based on imbeddings in vector-valued sequence spaces to obtain atomic decompositions of the predual of Qp . This last result is then extended to the real variable setting where we prove atomic decomposition theorems for the preduals of certain function spaces that generalize .