A counterexample for local smoothing for averages over curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908360774778880 |
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| author | Beltran, David Hickman, Jonathan |
| author_facet | Beltran, David Hickman, Jonathan |
| contents | We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in $\mathbb{R}^n$ for $n \geq 3$. This demonstrates a limitation in the strength of local smoothing estimates towards establishing bounds for the corresponding maximal functions when $n \geq 5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counterexample for local smoothing for averages over curves Beltran, David Hickman, Jonathan Classical Analysis and ODEs 42B20, 42B25 We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in $\mathbb{R}^n$ for $n \geq 3$. This demonstrates a limitation in the strength of local smoothing estimates towards establishing bounds for the corresponding maximal functions when $n \geq 5$. |
| title | A counterexample for local smoothing for averages over curves |
| topic | Classical Analysis and ODEs 42B20, 42B25 |
| url | https://arxiv.org/abs/2505.07788 |