Lebesgue bounds for multilinear spherical and lacunary maximal averages
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917289445556224 |
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| author | Gao, Xinyu |
| author_facet | Gao, Xinyu |
| contents | We establish $L^{p_1}(\mathbb R^d) \times \cdots \times L^{p_n}(\mathbb R^d) \rightarrow L^r(\mathbb R^d)$ bounds for spherical averaging operators $\mathcal A^n$ in dimensions $d \geq 2$ for indices $1\le p_1,\dots , p_n\le \infty$ and $\frac{1}{p_1}+\cdots +\frac{1}{p_n}=\frac{1}{r}$. We obtain this result by first showing that $\mathcal A^n$ maps $L^1 \times \cdots \times L^1 \rightarrow L^1$. We also obtain similar estimates for lacunary maximal spherical averages in the largest possible open region of indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lebesgue bounds for multilinear spherical and lacunary maximal averages Gao, Xinyu Classical Analysis and ODEs We establish $L^{p_1}(\mathbb R^d) \times \cdots \times L^{p_n}(\mathbb R^d) \rightarrow L^r(\mathbb R^d)$ bounds for spherical averaging operators $\mathcal A^n$ in dimensions $d \geq 2$ for indices $1\le p_1,\dots , p_n\le \infty$ and $\frac{1}{p_1}+\cdots +\frac{1}{p_n}=\frac{1}{r}$. We obtain this result by first showing that $\mathcal A^n$ maps $L^1 \times \cdots \times L^1 \rightarrow L^1$. We also obtain similar estimates for lacunary maximal spherical averages in the largest possible open region of indices. |
| title | Lebesgue bounds for multilinear spherical and lacunary maximal averages |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.11255 |