Five-Linear Singular Integral Estimates of Brascamp-Lieb Type

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 to develop a sufficiently general technique to estimate singular integral variants of Brascamp-Lieb inequalities that do not obey H\"older scaling. The...

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Bibliographic Details
Published inarXiv.org
Main Authors Muscalu, Camil, Zhai, Yujia
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.01.2021
Subjects
Integrals
Mathematics - Classical Analysis and ODEs
Subspaces
Tensors
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Summary: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 to develop a sufficiently general technique to estimate singular integral variants of Brascamp-Lieb inequalities that do not obey H\"older 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.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.09064