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arXiv · 2211.06055

A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains

Mattia Calzi
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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 $H^2$; 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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Mattia Calzi. 2022-11-11. A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains. https://doi.org/10.1007/978-981-95-5280-1_3

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