Survey presenting old and new results on invariant Hilbert, semi-Hilbert, Banach and semi-Banach spaces of holomorphic functions on symmetric domains including weighted Bergman, Hardy, Dirichlet, Besov and Bloch spaces.
Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains
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abstract
In this paper we consider a symmetric Siegel domain $D$ and some natural representations of the M\"obius group $G$ of its biholomorphisms and of the group $\mathrm{Aff}$ of its affine biholomorphisms. We provide a complete classification of the affinely-invariant semi-Hilbert spaces (satisfying some natural additional assumptions) on tube domains, and improve the classification of M\"obius-invariant Semi-Hilbert spaces on general domains.
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2022 1verdicts
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A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains
Survey presenting old and new results on invariant Hilbert, semi-Hilbert, Banach and semi-Banach spaces of holomorphic functions on symmetric domains including weighted Bergman, Hardy, Dirichlet, Besov and Bloch spaces.