Sharp bilinear estimates for maximal singular integrals with kernels in weighted $L^q$ spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917032371421184 |
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| author | Lappas, Stefanos Park, Bae Jun |
| author_facet | Lappas, Stefanos Park, Bae Jun |
| contents | In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to L^{p}(\mathbb{R})$ estimates in the full quasi-Banach range of exponents $1 < p_1, p_2 < \infty$ and $1/2 < p < \infty$. Our approach extends and unifies several recent contributions, including those of Honzík, the first author, and Slavíkova, as well as the second author in the bilinear and in the one-dimensional settings, by allowing the angular component $Ω$ of the kernel to belong to weighted $L^q$-spaces on $\mathbb{S}^1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp bilinear estimates for maximal singular integrals with kernels in weighted $L^q$ spaces Lappas, Stefanos Park, Bae Jun Classical Analysis and ODEs 42B20, 42B25, 47H60 In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to L^{p}(\mathbb{R})$ estimates in the full quasi-Banach range of exponents $1 < p_1, p_2 < \infty$ and $1/2 < p < \infty$. Our approach extends and unifies several recent contributions, including those of Honzík, the first author, and Slavíkova, as well as the second author in the bilinear and in the one-dimensional settings, by allowing the angular component $Ω$ of the kernel to belong to weighted $L^q$-spaces on $\mathbb{S}^1$. |
| title | Sharp bilinear estimates for maximal singular integrals with kernels in weighted $L^q$ spaces |
| topic | Classical Analysis and ODEs 42B20, 42B25, 47H60 |
| url | https://arxiv.org/abs/2510.19184 |