Holomorphic Function Spaces on Homogeneous Siegel Domains

TL;DR

This paper investigates various aspects of holomorphic function spaces on homogeneous Siegel domains, including Bergman spaces, Hardy spaces, and boundary behaviors, extending classical results to a broader class of domains.

Contribution

It introduces a comprehensive analysis of weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II, generalizing previous results from specific cases.

Findings

Established sampling and atomic decomposition results.

Analyzed duality and boundary value problems.

Proved boundedness of Bergman projectors on these 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.