On the Theory of Bergman Spaces on Homogeneous Siegel Domains

TL;DR

This paper compares and completes the theory of mixed normed Bergman spaces on homogeneous Siegel domains, addressing various properties like inclusions, duality, and boundary behavior.

Contribution

It unifies and extends existing results in one of the main approaches to Bergman spaces on homogeneous Siegel domains.

Findings

Established natural inclusions and density results

Proved completeness and reproducing properties

Analyzed boundary values and transference techniques

Abstract

We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the literature and complete the existing ones in one of the two settings. The results we present are: natural inclusions, density, completeness, reproducing properties, sampling, atomic decomposition, duality, continuity of Bergman projectors, boundary values, transference.