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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.14635 |
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| _version_ | 1866909542244155392 |
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| author | Zhang, Jianghao |
| author_facet | Zhang, Jianghao |
| contents | We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving $L^p$ bounds increases with the rank $\frac{m}{d}$, and our focus is on the fractional rank case $\frac{m}{d}<\frac{n}{2}\leq \lceil \frac{m}{d}\rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Degenerate Multilinear Singular Multipliers with Fractional Rank Zhang, Jianghao Classical Analysis and ODEs We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving $L^p$ bounds increases with the rank $\frac{m}{d}$, and our focus is on the fractional rank case $\frac{m}{d}<\frac{n}{2}\leq \lceil \frac{m}{d}\rceil$. |
| title | Non-Degenerate Multilinear Singular Multipliers with Fractional Rank |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.14635 |