Sharp $L^p$ bounds for the helical maximal function
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911078644973568 |
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| author | Beltran, David Guo, Shaoming Hickman, Jonathan Seeger, Andreas |
| author_facet | Beltran, David Guo, Shaoming Hickman, Jonathan Seeger, Andreas |
| contents | We establish the $L^p(\mathbb{R}^3)$ boundedness of the helical maximal function for the sharp range $p>3$. Our results improve the previous known bounds for $p>4$. The key ingredient is a new microlocal smoothing estimate for averages along dilates of the helix, which is established via a square function analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08272 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Sharp $L^p$ bounds for the helical maximal function Beltran, David Guo, Shaoming Hickman, Jonathan Seeger, Andreas Classical Analysis and ODEs We establish the $L^p(\mathbb{R}^3)$ boundedness of the helical maximal function for the sharp range $p>3$. Our results improve the previous known bounds for $p>4$. The key ingredient is a new microlocal smoothing estimate for averages along dilates of the helix, which is established via a square function analysis. |
| title | Sharp $L^p$ bounds for the helical maximal function |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2102.08272 |