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Five-linear singular
integral estimates of Brascamp–Lieb-type
Camil Muscalu and Yujia Zhai |
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Vol. 15 (2022), No. 4, 1011–1095
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Abstract |
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We prove the full range of estimates for a five-linear singular integral of Brascamp–Lieb type. The study is methodology-oriented with the goal of developing a sufficiently general technique to estimate singular integral variants of Brascamp–Lieb inequalities that do not obey Hölder scaling. The invented methodology constructs localized analysis on the entire space from local information on its subspaces of lower dimensions and combines such tensor-type arguments with the generic localized analysis. A direct consequence of the boundedness of the five-linear singular integral is a Leibniz rule which captures nonlinear interactions of waves from transversal directions. |
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Keywords
multilinear and multiparameter operators, Brascamp–Lieb
singular integrals, non-Hölder scaling, Leibniz rule,
tensor-type stopping-time decompositions
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Mathematical Subject Classification 2010
Primary: 42A45, 42B15, 42B20, 42B25, 42B37
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Milestones
Received: 25 January 2020
Revised: 10 October 2020
Accepted: 31 December 2020
Published: 3 September 2022
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Authors |
| Camil Muscalu | |
| Department of Mathematics Cornell University Ithaca, NY United States |
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| Yujia Zhai | |
| Laboratoire de Mathématiques Université de Nantes Nantes France |
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