Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis

Jonathan Bennett; Richard Bez

doi:10.1016/j.jfa.2010.07.015

Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis

Jonathan Bennett, Richard Bez

Mathematics

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21 Citations (Scopus)

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Abstract

We use the method of induction-on-scales to prove certain diffeomorphism-invariant nonlinear Brascamp-Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru-Herr-Tataru and Bennett-Carbery-Wright. (C) 2010 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	2520-2556
Number of pages	37
Journal	Journal of Functional Analysis
Volume	259
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2010.07.015
Publication status	Published - 15 Nov 2010

Keywords

Fourier extension estimates
Brascamp-Lieb inequalities
Induction-on-scales

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10.1016/j.jfa.2010.07.015

NonlinearBL PUREversionAccepted author manuscript, 290 KB

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Bennett, J.
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils

Cite this

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title = "Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis",

abstract = "We use the method of induction-on-scales to prove certain diffeomorphism-invariant nonlinear Brascamp-Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru-Herr-Tataru and Bennett-Carbery-Wright. (C) 2010 Elsevier Inc. All rights reserved.",

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AU - Bez, Richard

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AB - We use the method of induction-on-scales to prove certain diffeomorphism-invariant nonlinear Brascamp-Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru-Herr-Tataru and Bennett-Carbery-Wright. (C) 2010 Elsevier Inc. All rights reserved.

KW - Fourier extension estimates

KW - Brascamp-Lieb inequalities

KW - Induction-on-scales

U2 - 10.1016/j.jfa.2010.07.015

DO - 10.1016/j.jfa.2010.07.015

M3 - Article

VL - 259

SP - 2520

EP - 2556

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

Some nonlinear Brascamp–Lieb inequalities and applications to harmonic analysis

Abstract

Keywords

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Projects

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics

Cite this