Compactness of composition operators on the Bergman space of the bidisc
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909695202033664 |
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| author | Clos, Timothy G. Cuckovic, Zeljko Sahutoglu, Sonmez |
| author_facet | Clos, Timothy G. Cuckovic, Zeljko Sahutoglu, Sonmez |
| contents | Let $φ$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_φ$ is compact on the Bergman space if and only if $φ(\overline{\mathbb{D}^2})\cap \mathbb{T}^2=\emptyset$ and $φ(\overline{\mathbb{D}^2}\setminus \mathbb{T}^2)\cap b\mathbb{D}^2=\emptyset$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactness of composition operators on the Bergman space of the bidisc Clos, Timothy G. Cuckovic, Zeljko Sahutoglu, Sonmez Complex Variables Functional Analysis 47B33, 32A36 Let $φ$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_φ$ is compact on the Bergman space if and only if $φ(\overline{\mathbb{D}^2})\cap \mathbb{T}^2=\emptyset$ and $φ(\overline{\mathbb{D}^2}\setminus \mathbb{T}^2)\cap b\mathbb{D}^2=\emptyset$. |
| title | Compactness of composition operators on the Bergman space of the bidisc |
| topic | Complex Variables Functional Analysis 47B33, 32A36 |
| url | https://arxiv.org/abs/2409.09529 |