A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910147320741888 |
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| author | Calzi, Mattia |
| author_facet | Calzi, Mattia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06055 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains Calzi, Mattia Complex Variables Functional Analysis 46E15, 47B33, 32M15 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. |
| title | A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains |
| topic | Complex Variables Functional Analysis 46E15, 47B33, 32M15 |
| url | https://arxiv.org/abs/2211.06055 |