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arXiv · 2603.23238

Maximal growth of the Stein-Wainger oscillatory integral

Cheng Zhang·Zhifei Zhu
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Abstract

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.

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Cheng Zhang, Zhifei Zhu. 2026-03-24. Maximal growth of the Stein-Wainger oscillatory integral. https://arxiv.org/abs/2603.23238

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