Sharp local smoothing estimates for curve averages
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913963596316672 |
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| author | Gan, Shengwen Maldague, Dominique Oh, Changkeun |
| author_facet | Gan, Shengwen Maldague, Dominique Oh, Changkeun |
| contents | 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. There are new ingredients in the proof: Fourier decay estimates and wave envelope estimates for nondegenerate curves in $\mathbb{R}^n$. As a byproduct, we prove Bochner-Riesz estimates for nondegenerate curves in all dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp local smoothing estimates for curve averages Gan, Shengwen Maldague, Dominique Oh, Changkeun Classical Analysis and ODEs Analysis of PDEs 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. There are new ingredients in the proof: Fourier decay estimates and wave envelope estimates for nondegenerate curves in $\mathbb{R}^n$. As a byproduct, we prove Bochner-Riesz estimates for nondegenerate curves in all dimensions. |
| title | Sharp local smoothing estimates for curve averages |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2507.09696 |