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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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Table of 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.