Holomorphic function spaces on homogeneous siegel domains

We study several connected problems concerning holomorphic function spaces on homogeneous Siegel domains. The main object of our study is the class of weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. The problems considered include: sampling, atomic decomposition, duality, boundary values, and boundedness of the Bergman projectors. Our analysis covers the Hardy spaces, and suitable generalizations of the classical Bloch and Dirichlet spaces. One of the main novelties in this work is the generality of the domains under consideration, that is, homogeneous Siegel domains, extending many results from the more particular cases of the upper half-plane, Siegel domains of tube type over irreducible cones, or symmetric, irreducible Siegel domains of type II.