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arXiv · 2507.09696

Sharp local smoothing estimates for curve averages

Shengwen Gan·Dominique Maldague·Changkeun Oh
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Abstract

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^p$ boundedness of the helical maximal operator in $\mathbb{R}^4$, which was previously known only for $\mathbb{R}^2$ and $\mathbb{R}^3$. We also improve previously known results in higher dimensions. The main new ingredient is a novel wave envelope estimate adapted to moment curves, which is a powerful tool in the proof of the local smoothing estimate.

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Shengwen Gan, Dominique Maldague, Changkeun Oh. 2025-07-13. Sharp local smoothing estimates for curve averages. https://arxiv.org/abs/2507.09696

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