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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2604.20326 |
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| _version_ | 1866918528676790272 |
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| author | Jin, Jianjun |
| author_facet | Jin, Jianjun |
| contents | In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. This extends a related result by Shimorin. The proof of our new theorem relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work. We finally point out that the Koebe function is still the extremal function for certain higher-order Schwarzians of the univalent functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20326 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function Jin, Jianjun Complex Variables 47A30, 30C35, 30H20 In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. This extends a related result by Shimorin. The proof of our new theorem relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work. We finally point out that the Koebe function is still the extremal function for certain higher-order Schwarzians of the univalent functions. |
| title | Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function |
| topic | Complex Variables 47A30, 30C35, 30H20 |
| url | https://arxiv.org/abs/2604.20326 |