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.

31 pages, no figures

References in corpus (6)

• Toeplitz and Cesàro-Type Operators on Homogeneous Siegel Domains
• Besov Spaces of Analytic Type: Interpolation, Convolution, Fourier Multipliers, Inclusions
• Bernstein Spaces on Siegel CR Manifolds
• Boundedness of Bergman projectors on homogeneous Siegel domains
• Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds
• Paley-Wiener-Schwartz Theorems on Quadratic CR Manifolds