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Holomorphic function spaces on homogeneous Siegel domains

Volume 563 / 2021

Mattia Calzi, Marco M. Peloso Dissertationes Mathematicae 563 (2021), 1-168 MSC: Primary 42B35; Secondary 32M15. DOI: 10.4064/dm833-3-2021 Published online: 4 August 2021

Abstract

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.

Authors

  • Mattia CalziDipartimento di Matematica
    Università degli Studi di Milano
    Via C. Saldini 50
    20133 Milano, Italy
    e-mail
  • Marco M. PelosoDipartimento di Matematica
    Università degli Studi di Milano
    Via C. Saldini 50
    20133 Milano, Italy
    e-mail

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