The Bloch Space over the Upper Half-Plane

Abstract

In this paper, we represent Bloch functions over the upper half-plane as integrals involving modified Bergman reproducing kernels. This enables us to obtain a precise characterization of the dual space of the Bergman space A1(Π+) in terms of the normalized Bloch space Bi(Π+). Furthermore, we show conversely that the predual of the Bergman space A1(Π+) can be characterized by the little normalized Bloch space Bi,0(Π+).