A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform"
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917707960549376 |
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| author | Hsu, Martin Lin, Fred Yu-Hsiang Stokolosa, Amelia |
| author_facet | Hsu, Martin Lin, Fred Yu-Hsiang Stokolosa, Amelia |
| contents | This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy model of a Hilbert transform along a parabola. These standard techniques prove to be insufficient in the study of the triangular Hilbert transform with curvature. The central and novel idea in their proof of the $L^p$-boundedness of the triangular Hilbert transform with curvature is a trilinear smoothing inequality which we also examine in this article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" Hsu, Martin Lin, Fred Yu-Hsiang Stokolosa, Amelia Classical Analysis and ODEs Primary: 42B20, Secondary: 42B15, 42B25 This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy model of a Hilbert transform along a parabola. These standard techniques prove to be insufficient in the study of the triangular Hilbert transform with curvature. The central and novel idea in their proof of the $L^p$-boundedness of the triangular Hilbert transform with curvature is a trilinear smoothing inequality which we also examine in this article. |
| title | A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" |
| topic | Classical Analysis and ODEs Primary: 42B20, Secondary: 42B15, 42B25 |
| url | https://arxiv.org/abs/2311.11391 |