Sharp estimates for oscillatory integral operators via polynomial partitioning
The sharp range of L -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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International Press of Boston
2021
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| Online Access: | https://hdl.handle.net/1721.1/136252 |
| _version_ | 1826195839717998592 |
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| author | Guth, Larry Hickman, Jonathan Iliopoulou, Marina |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guth, Larry Hickman, Jonathan Iliopoulou, Marina |
| author_sort | Guth, Larry |
| collection | MIT |
| description | The sharp range of L -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments. The main result implies improved bounds for the Bochner–Riesz conjecture in dimensions (Formula Presented). p |
| first_indexed | 2024-09-23T10:16:16Z |
| format | Article |
| id | mit-1721.1/136252 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:16:16Z |
| publishDate | 2021 |
| publisher | International Press of Boston |
| record_format | dspace |
| spelling | mit-1721.1/1362522024-01-03T18:05:20Z Sharp estimates for oscillatory integral operators via polynomial partitioning Guth, Larry Hickman, Jonathan Iliopoulou, Marina Massachusetts Institute of Technology. Department of Mathematics The sharp range of L -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments. The main result implies improved bounds for the Bochner–Riesz conjecture in dimensions (Formula Presented). p 2021-10-27T20:34:31Z 2021-10-27T20:34:31Z 2019 2021-05-20T14:06:18Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136252 en 10.4310/ACTA.2019.V223.N2.A2 Acta Mathematica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf International Press of Boston arXiv |
| spellingShingle | Guth, Larry Hickman, Jonathan Iliopoulou, Marina Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title | Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title_full | Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title_fullStr | Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title_full_unstemmed | Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title_short | Sharp estimates for oscillatory integral operators via polynomial partitioning |
| title_sort | sharp estimates for oscillatory integral operators via polynomial partitioning |
| url | https://hdl.handle.net/1721.1/136252 |
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