Hardy spaces of operator-valued analytic functions

Abstract

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operator-valued H-1-BMOA duality theorem is proved. Finally, by the H-1-BMOA duality we present the Lusin area integral and Littlewood-Paley g-function characterizations of the operator-valued analytic Hardy space.