Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917208164139008 |
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| author | Fraccaroli, Marco Saari, Olli Thiele, Christoph |
| author_facet | Fraccaroli, Marco Saari, Olli Thiele, Christoph |
| contents | We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that are push-forwards by $K$-quasiconformal matrices of suitable symbols. As particular applications, our result recovers the uniform bounds for the one-dimensional bilinear Hilbert transforms in the strict local $L^{2}$ range, and it implies the uniform bounds for two-dimensional bilinear Beurling transforms, which are new, in the same range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity Fraccaroli, Marco Saari, Olli Thiele, Christoph Classical Analysis and ODEs We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that are push-forwards by $K$-quasiconformal matrices of suitable symbols. As particular applications, our result recovers the uniform bounds for the one-dimensional bilinear Hilbert transforms in the strict local $L^{2}$ range, and it implies the uniform bounds for two-dimensional bilinear Beurling transforms, which are new, in the same range. |
| title | Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2402.11661 |