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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.27588 |
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| _version_ | 1866910263693803520 |
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| author | Pandis, Christos |
| author_facet | Pandis, Christos |
| contents | We prove that the set of integrable functions on the unit circle for which the analogue of Paley's theorem for $H^1$ fails is residual in $L^1(\mathbb T)$. Moreover, we establish algebraic genericity and spaceability results in several Hardy-type function spaces under prescribed conditions on Taylor coefficients, extending phenomena considered in \cite{pandis2024some,NestoridisGenericH1}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27588 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological Genericity and Large Linear Structures in Function Spaces Pandis, Christos Complex Variables Functional Analysis We prove that the set of integrable functions on the unit circle for which the analogue of Paley's theorem for $H^1$ fails is residual in $L^1(\mathbb T)$. Moreover, we establish algebraic genericity and spaceability results in several Hardy-type function spaces under prescribed conditions on Taylor coefficients, extending phenomena considered in \cite{pandis2024some,NestoridisGenericH1}. |
| title | Topological Genericity and Large Linear Structures in Function Spaces |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2605.27588 |