On the Theory of Bergman Spaces on Homogeneous Siegel Domains

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.