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15 November 2020 On the nonlinear Brascamp–Lieb inequality
Jonathan Bennett, Neal Bez, Stefan Buschenhenke, Michael G. Cowling, Taryn C. Flock
Duke Math. J. 169(17): 3291-3338 (15 November 2020). DOI: 10.1215/00127094-2020-0027

Abstract

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.

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Jonathan Bennett. Neal Bez. Stefan Buschenhenke. Michael G. Cowling. Taryn C. Flock. "On the nonlinear Brascamp–Lieb inequality." Duke Math. J. 169 (17) 3291 - 3338, 15 November 2020. https://doi.org/10.1215/00127094-2020-0027

Information

Received: 19 February 2019; Revised: 20 February 2020; Published: 15 November 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4173156
Digital Object Identifier: 10.1215/00127094-2020-0027

Subjects:
Primary: 42B37
Secondary: 44A12, 52A40

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 17 • 15 November 2020
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