A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains

2022/11/11 by Calzi, Mattia
#32M15 #46E15 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.06055

Abstract

We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces include: weighted Bergman spaces; the Hardy space H²; the Dirichlet space; holomorphic Besov spaces; the Bloch space. Our main focus will be on invariant Hilbert and semi-Hilbert spaces, but we shall also discuss minimal and maximal spaces in suitable classes of invariant Banach and semi-Banach spaces.

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