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

TL;DR

This paper introduces a Bloch-type space on the Siegel upper half-space and establishes its role as the predual of the Bergman space $A_ u^1$, advancing understanding of duality in complex analysis.

Contribution

It defines a new Bloch-type space and proves it is the predual of the Bergman space $A_ u^1$ on the Siegel upper half-space.

Findings

Identification of the predual space of $A_ u^1$ as a Bloch-type space

Establishment of duality pairing between these spaces

Characterization of the little Bloch-type space $ ilde{calB}_0$

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.