A Bloch-type space and the predual of $A_{\lambda }^1$ on the Siegel upper half-space

Abstract

This paper aims to determine the predual of the Bergman space $A_{\lambda }^1$ on the Siegel upper half-space. To achieve this, a Bloch-type space $\widetilde{\calB}$ is introduced and studied, and some of its essential properties are established. We identify the little Bloch-type space $\widetilde{\calB}_0$ with the predual of $A_{\lambda }^1$ via a duality pairing.

15 pages