Sharp Fourier restriction to monomial curves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866913578969202688 |
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| author | Biswas, Chandan Stovall, Betsy |
| author_facet | Biswas, Chandan Stovall, Betsy |
| contents | We establish lower bounds for the operator norms of the Fourier restriction/extension operators associated to monomial curves with affine arclength measure. Furthermore, we prove that the set of all extremizing sequences of such an operator is precompact modulo the operator's symmetry group if and only if the operator norm is strictly larger than this threshold. For the proof, we introduce a number of new ingredients, some of which may be applicable to analogous questions on more general manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05317 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp Fourier restriction to monomial curves Biswas, Chandan Stovall, Betsy Classical Analysis and ODEs We establish lower bounds for the operator norms of the Fourier restriction/extension operators associated to monomial curves with affine arclength measure. Furthermore, we prove that the set of all extremizing sequences of such an operator is precompact modulo the operator's symmetry group if and only if the operator norm is strictly larger than this threshold. For the proof, we introduce a number of new ingredients, some of which may be applicable to analogous questions on more general manifolds. |
| title | Sharp Fourier restriction to monomial curves |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2302.05317 |