A degree one Carleson operator along the paraboloid
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908569865027584 |
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| author | Becker, Lars |
| author_facet | Becker, Lars |
| contents | We prove $L^p$ bounds, $\frac{d^2 + 4d + 2}{(d+1)^2} < p < 2(d+1)$, for maximal linear modulations of singular integrals along paraboloids with frequencies in certain subspaces of $\mathbb{R}^{d+1}$, for $d \geq 2$. This generalizes Carleson's theorem on convergence of Fourier series, and complements a corresponding result by Pierce and Yung with polynomial modulations without linear terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01134 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A degree one Carleson operator along the paraboloid Becker, Lars Classical Analysis and ODEs 42B20 We prove $L^p$ bounds, $\frac{d^2 + 4d + 2}{(d+1)^2} < p < 2(d+1)$, for maximal linear modulations of singular integrals along paraboloids with frequencies in certain subspaces of $\mathbb{R}^{d+1}$, for $d \geq 2$. This generalizes Carleson's theorem on convergence of Fourier series, and complements a corresponding result by Pierce and Yung with polynomial modulations without linear terms. |
| title | A degree one Carleson operator along the paraboloid |
| topic | Classical Analysis and ODEs 42B20 |
| url | https://arxiv.org/abs/2312.01134 |