Curved commutators in the plane
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911795780780032 |
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| author | Li, Kangwei Martikainen, Henri Oikari, Tuomas |
| author_facet | Li, Kangwei Martikainen, Henri Oikari, Tuomas |
| contents | We complete the $L^p$ boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers all monomial curves while previous results had significant geometric restrictions. We also, for the first time, develop the corresponding necessity theory for curves with non-vanishing torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curved commutators in the plane Li, Kangwei Martikainen, Henri Oikari, Tuomas Classical Analysis and ODEs 42B20 We complete the $L^p$ boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers all monomial curves while previous results had significant geometric restrictions. We also, for the first time, develop the corresponding necessity theory for curves with non-vanishing torsion. |
| title | Curved commutators in the plane |
| topic | Classical Analysis and ODEs 42B20 |
| url | https://arxiv.org/abs/2403.08338 |