On the nonlinear Brascamp-Lieb inequality

Jonathan Bennett, Neal Bez, Stefan Buschenhenke, Michael G. Cowling, Taryn C. Flock

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We prove a nonlinear variant of the general Brascamp–Lieb inequality. Our proof consists of running an efficient, or “tight,” induction-on-scales argument, which uses the existence of Gaussian near-extremizers to the underlying linear Brascamp–Lieb inequality (Lieb’s theorem) in a fundamental way. A key ingredient is an effective version of Lieb’s theorem, which we establish via a careful analysis of near-minimizers of weighted sums of exponential functions. Instances of this inequality are quite prevalent in mathematics, and we illustrate this with some applications in harmonic analysis.
Original languageEnglish
Pages (from-to)3291-3338
Number of pages48
JournalDuke Mathematical Journal
Issue number17
Early online date16 Oct 2020
Publication statusPublished - 15 Nov 2020

Bibliographical note

39 pages. This article subsumes the results of arXiv:1801.05214 (https://arxiv.org/abs/1801.05214). Not yet published as of 02/11/2020.


  • math.CA
  • 42B37, 44A12, 52A40


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