A sharp Hörmander condition for bilinear Fourier multipliers with Lipschitz singularities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913257246162944 |
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| author | Chen, Jiao Hsu, Martin Lin, Fred Yu-Hsiang |
| author_facet | Chen, Jiao Hsu, Martin Lin, Fred Yu-Hsiang |
| contents | This paper studies the $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ range. We assume a Hörmander condition relative to a singular set that is a finite union of Lipschitz curves. The Hörmander condition is sharp with respect to the Sobolev exponent. Our setup generalizes the non-degenerate bilinear Hilbert transform but avoids issues of uniform bounds near degeneracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sharp Hörmander condition for bilinear Fourier multipliers with Lipschitz singularities Chen, Jiao Hsu, Martin Lin, Fred Yu-Hsiang Classical Analysis and ODEs This paper studies the $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ range. We assume a Hörmander condition relative to a singular set that is a finite union of Lipschitz curves. The Hörmander condition is sharp with respect to the Sobolev exponent. Our setup generalizes the non-degenerate bilinear Hilbert transform but avoids issues of uniform bounds near degeneracy. |
| title | A sharp Hörmander condition for bilinear Fourier multipliers with Lipschitz singularities |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.04721 |