Sparse domination for rough multilinear singular integrals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912444057649152 |
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| author | Dan, Binwei Xue, Qingying |
| author_facet | Dan, Binwei Xue, Qingying |
| contents | Let $Ω$ be a function on $\mathbb{R}^{mn} $, homogeneous of degree zero, and satisfy a cancellation condition on the unit sphere $\mathbb{S}^{mn-1}$. In this paper, we show that the multilinear singular integral operator
\[
\mathcal{T}_Ω(f_1, \ldots, f_m)(x) := \mathrm{p.v.} \int_{\mathbb{R}^{mn}} \frac{Ω(x - y_1, \ldots, x - y_m)}{|x - \vec{y}|^{mn}} \prod_{i=1}^m f_i(y_i) \, d\vec{y},
\]
associated with a rough kernel $Ω\in L^r(\mathbb{S}^{mn-1}) $, $r > 1 $, admits a sparse domination, where $\quad \vec{y}=(y_1,\ldots,y_m)$ and $ d\vec{y}=dy_1\cdots dy_m$. As a consequence, we derive some {quantitative weighted norm inequalities} for $ \mathcal{T}_Ω $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse domination for rough multilinear singular integrals Dan, Binwei Xue, Qingying Classical Analysis and ODEs 42B20 Let $Ω$ be a function on $\mathbb{R}^{mn} $, homogeneous of degree zero, and satisfy a cancellation condition on the unit sphere $\mathbb{S}^{mn-1}$. In this paper, we show that the multilinear singular integral operator \[ \mathcal{T}_Ω(f_1, \ldots, f_m)(x) := \mathrm{p.v.} \int_{\mathbb{R}^{mn}} \frac{Ω(x - y_1, \ldots, x - y_m)}{|x - \vec{y}|^{mn}} \prod_{i=1}^m f_i(y_i) \, d\vec{y}, \] associated with a rough kernel $Ω\in L^r(\mathbb{S}^{mn-1}) $, $r > 1 $, admits a sparse domination, where $\quad \vec{y}=(y_1,\ldots,y_m)$ and $ d\vec{y}=dy_1\cdots dy_m$. As a consequence, we derive some {quantitative weighted norm inequalities} for $ \mathcal{T}_Ω $. |
| title | Sparse domination for rough multilinear singular integrals |
| topic | Classical Analysis and ODEs 42B20 |
| url | https://arxiv.org/abs/2506.17905 |