Compact composition operators on model spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911372898467840 |
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| author | Doubtsov, Evgueni |
| author_facet | Doubtsov, Evgueni |
| contents | Let $φ: B_d\to\mathbb{D}$, $d\ge 1$, be a holomorphic function, where $B_d$ denotes the open unit ball of $\mathbb{C}^d$ and $\mathbb{D}= B_1$. Let $Θ: \mathbb{D} \to \mathbb{D}$ be an inner function and let $K^p_Θ$ denote the corresponding model space. For $p>1$, we characterize the compact composition operators $C_φ: K^p_Θ\to H^p(B_d)$, where $H^p(B_d)$ denotes the Hardy space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact composition operators on model spaces Doubtsov, Evgueni Complex Variables Functional Analysis 47B33, 32A35, 46B70 Let $φ: B_d\to\mathbb{D}$, $d\ge 1$, be a holomorphic function, where $B_d$ denotes the open unit ball of $\mathbb{C}^d$ and $\mathbb{D}= B_1$. Let $Θ: \mathbb{D} \to \mathbb{D}$ be an inner function and let $K^p_Θ$ denote the corresponding model space. For $p>1$, we characterize the compact composition operators $C_φ: K^p_Θ\to H^p(B_d)$, where $H^p(B_d)$ denotes the Hardy space. |
| title | Compact composition operators on model spaces |
| topic | Complex Variables Functional Analysis 47B33, 32A35, 46B70 |
| url | https://arxiv.org/abs/2404.08140 |