Recovering Hardy spaces from optimal domains of integration operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911682836561920 |
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| author | Eskandari, Setareh Perälä, Antti |
| author_facet | Eskandari, Setareh Perälä, Antti |
| contents | We study the optimal domains for bounded Volterra integration operators $T_g$ between Hardy spaces $H^p$ and $H^q$ of the unit ball. It is shown that the optimal domain of a bounded $T_g:H^p\to H^q$ always strictly contains $H^p$. Moreover, the intersection of the optimal domains is equal to $H^p$ if $p\geq q$, whereas if $p<q$, we show that this intersection is a genuinely larger tent space of holomorphic functions. In the unit disk, this problem was recently solved for $p=q$ by Bellavita, Daskalogiannis, Nikolaidis and Stylogiannis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_11955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recovering Hardy spaces from optimal domains of integration operators Eskandari, Setareh Perälä, Antti Complex Variables Functional Analysis 30H10, 47G10 We study the optimal domains for bounded Volterra integration operators $T_g$ between Hardy spaces $H^p$ and $H^q$ of the unit ball. It is shown that the optimal domain of a bounded $T_g:H^p\to H^q$ always strictly contains $H^p$. Moreover, the intersection of the optimal domains is equal to $H^p$ if $p\geq q$, whereas if $p<q$, we show that this intersection is a genuinely larger tent space of holomorphic functions. In the unit disk, this problem was recently solved for $p=q$ by Bellavita, Daskalogiannis, Nikolaidis and Stylogiannis. |
| title | Recovering Hardy spaces from optimal domains of integration operators |
| topic | Complex Variables Functional Analysis 30H10, 47G10 |
| url | https://arxiv.org/abs/2602.11955 |