  We study several connected problems of holomorphic function spaces on
homogeneous Siegel domains. The main object of our study concerns weighted
mixed norm Bergman spaces on homogeneous Siegel domains of type II. These
problems include: sampling, atomic decomposition, duality, boundary values,
boundedness of the Bergman projectors. Our analysis include 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.
