On the nonlinear Brascamp-Lieb inequality

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

doi:10.1215/00127094-2020-0027

On the nonlinear Brascamp-Lieb inequality

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

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

373 Downloads (Pure)

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.

Original language	English
Pages (from-to)	3291-3338
Number of pages	48
Journal	Duke Mathematical Journal
Volume	169
Issue number	17
Early online date	16 Oct 2020
DOIs	https://doi.org/10.1215/00127094-2020-0027
Publication status	Published - 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.

Keywords

math.CA
42B37, 44A12, 52A40

Access to Document

10.1215/00127094-2020-0027Licence: None: All rights reserved

Bennett_et_al_On_the_nonlinear_Duke_Mathematical_Journal_2020
This document is the Author Accepted Manuscript version of a published work which appears in its final form in Duke Mathematical Journal, copyright © 2020 Duke University Press. The final Version of Record can be found at: https://projecteuclid.org/download/imagefirstpage_1/euclid.dmj/1602813956
Accepted author manuscript, 444 KBLicence: None: All rights reserved

https://arxiv.org/abs/1811.11052Licence: Other (please provide link to licence statement

Cite this

@article{ab0c9463bf5c442a8fef30dccc7f8c59,

title = "On the nonlinear Brascamp-Lieb inequality",

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{\textquoteright}s theorem) in a fundamental way. A key ingredient is an effective version of Lieb{\textquoteright}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.",

keywords = "math.CA, 42B37, 44A12, 52A40",

author = "Jonathan Bennett and Neal Bez and Stefan Buschenhenke and Cowling, \{Michael G.\} and Flock, \{Taryn C.\}",

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.",

year = "2020",

month = nov,

day = "15",

doi = "10.1215/00127094-2020-0027",

language = "English",

volume = "169",

pages = "3291--3338",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "17",

}

TY - JOUR

T1 - On the nonlinear Brascamp-Lieb inequality

AU - Bennett, Jonathan

AU - Bez, Neal

AU - Buschenhenke, Stefan

AU - Cowling, Michael G.

AU - Flock, Taryn C.

N1 - 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.

PY - 2020/11/15

Y1 - 2020/11/15

N2 - 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.

AB - 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.

KW - math.CA

KW - 42B37, 44A12, 52A40

UR - https://www.scopus.com/pages/publications/85096908396

U2 - 10.1215/00127094-2020-0027

DO - 10.1215/00127094-2020-0027

M3 - Article

SN - 0012-7094

VL - 169

SP - 3291

EP - 3338

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 17

ER -

On the nonlinear Brascamp-Lieb inequality

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this