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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23238 |
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| _version_ | 1866908909785055232 |
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| author | Zhang, Cheng Zhu, Zhifei |
| author_facet | Zhang, Cheng Zhu, Zhifei |
| contents | We establish a precise hierarchy for the maximal growth of the Stein-Wainger oscillatory integral as the regularity of the phase varies over Denjoy-Carleman classes, such as the Gevrey classes and their generalizations. In particular, we resolve a problem posed by Wang--Zhang, motivated by eigenfunction restriction estimates on curves, and also provide a new proof of a theorem of Nagel--Wainger on the Hilbert transform along curves. A key ingredient is the sharp estimate on the growth of a phase near a flat point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23238 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal growth of the Stein-Wainger oscillatory integral Zhang, Cheng Zhu, Zhifei Classical Analysis and ODEs Analysis of PDEs 42A45, 42B15, 42B20 We establish a precise hierarchy for the maximal growth of the Stein-Wainger oscillatory integral as the regularity of the phase varies over Denjoy-Carleman classes, such as the Gevrey classes and their generalizations. In particular, we resolve a problem posed by Wang--Zhang, motivated by eigenfunction restriction estimates on curves, and also provide a new proof of a theorem of Nagel--Wainger on the Hilbert transform along curves. A key ingredient is the sharp estimate on the growth of a phase near a flat point. |
| title | Maximal growth of the Stein-Wainger oscillatory integral |
| topic | Classical Analysis and ODEs Analysis of PDEs 42A45, 42B15, 42B20 |
| url | https://arxiv.org/abs/2603.23238 |