Holomorphic Function Spaces on Homogeneous Siegel Domains

Abstract

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.

135 pages + Corrigendum

Cited by in corpus (6)

• Carleson and reverse Carleson measures on homogeneous Siegel domains
• Besov Spaces of Analytic Type: Interpolation, Convolution, Fourier Multipliers, Inclusions
• Boundedness of Bergman projectors on homogeneous Siegel domains
• Sampling in spaces of entire functions of exponential type in ${\mathbb{C}}^{n+1}$
• Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds
• The Drury--Arveson space on the Siegel upper half-space and a von Neumann type inequality