The Grothendieck Theorem in Bergman Spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911247422717952 |
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| author | Liu, Yutao Wu, Jujie Xiong, Yuanpu |
| author_facet | Liu, Yutao Wu, Jujie Xiong, Yuanpu |
| contents | In this paper, we prove that if $E$ is a closed subspace of the holomorphic $L^p$-integrable space and is also contained in the holomorphic $L^q$-integrable space, for any $p > 1$ and any $q > p$, then the dimension of $E$ must be finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Grothendieck Theorem in Bergman Spaces Liu, Yutao Wu, Jujie Xiong, Yuanpu Complex Variables 32A36, 32A70 In this paper, we prove that if $E$ is a closed subspace of the holomorphic $L^p$-integrable space and is also contained in the holomorphic $L^q$-integrable space, for any $p > 1$ and any $q > p$, then the dimension of $E$ must be finite. |
| title | The Grothendieck Theorem in Bergman Spaces |
| topic | Complex Variables 32A36, 32A70 |
| url | https://arxiv.org/abs/2511.01521 |