Remarks on vector-valued BMOA and vector-valued multipliers

In this paper we consider the vector-valued interpretation of the space BMO A defined in terms of Carleson measures and analyze the relationship with t he one defined in terms of oscillation. We study the space of multipliers b etween H-p and BMOA in the vector-valued setting. This leads us to the cons ideration of some geometric properties depending upon the validity of certa in inequalities due to Littlewood and Paley on the g-function for vector-va lued functions.