Maximal estimates for averages over degenerate hypersurfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915087755771904 |
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| author | Oh, Sewook |
| author_facet | Oh, Sewook |
| contents | We study $L^p$ boundedness of the maximal average over dilations of a smooth hypersurface $S$. When the decay rate of the Fourier transform of a measure on $S$ is $1/2$, we establish the optimal maximal bound, which settles the conjecture raised by Stein. Additionally, when $S$ is not flat, we verify that the maximal average is bounded on $L^p$ for some finite $p$, which generalizes the result by Sogge and Stein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal estimates for averages over degenerate hypersurfaces Oh, Sewook Classical Analysis and ODEs 42B25, 42B20 We study $L^p$ boundedness of the maximal average over dilations of a smooth hypersurface $S$. When the decay rate of the Fourier transform of a measure on $S$ is $1/2$, we establish the optimal maximal bound, which settles the conjecture raised by Stein. Additionally, when $S$ is not flat, we verify that the maximal average is bounded on $L^p$ for some finite $p$, which generalizes the result by Sogge and Stein. |
| title | Maximal estimates for averages over degenerate hypersurfaces |
| topic | Classical Analysis and ODEs 42B25, 42B20 |
| url | https://arxiv.org/abs/2501.00858 |