Adjoint Brascamp–Lieb inequalities

Jonathan Bennett; Terence Tao

doi:10.1112/plms.12633

Adjoint Brascamp–Lieb inequalities

Jonathan Bennett^*, Terence Tao

^*Corresponding author for this work

Mathematics

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Abstract

The Brascamp-Lieb inequalities are a generalization of the Hölder, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of these inequalities, which can be viewed as an L^p version of the entropy Brascamp-Lieb inequalities of Carlen and Cordero-Erausquin. As applications, we reprove a log-convexity property of the Gowers uniformity norms, and establish some reverse L^p inequalities for various tomographic transforms. We conclude with some open questions.

Original language	English
Article number	e12633
Number of pages	51
Journal	Proceedings of the London Mathematical Society
Volume	129
Issue number	4
Early online date	14 Sept 2024
DOIs	https://doi.org/10.1112/plms.12633
Publication status	Published - Oct 2024

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10.1112/plms.12633Licence: Creative Commons: Attribution (CC BY)

BennettJ2024AdjointFinal published version, 426 KBLicence: Creative Commons: Attribution (CC BY)

Tomographic Fourier Analysis
Bennett, J.
Engineering & Physical Science Research Council
1/04/23 → 31/03/26
Project: Research Councils

Cite this

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title = "Adjoint Brascamp–Lieb inequalities",

abstract = "The Brascamp-Lieb inequalities are a generalization of the H{\"o}lder, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an {"}adjoint{"} version of these inequalities, which can be viewed as an Lp version of the entropy Brascamp-Lieb inequalities of Carlen and Cordero-Erausquin. As applications, we reprove a log-convexity property of the Gowers uniformity norms, and establish some reverse Lp inequalities for various tomographic transforms. We conclude with some open questions.",

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N2 - The Brascamp-Lieb inequalities are a generalization of the Hölder, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of these inequalities, which can be viewed as an Lp version of the entropy Brascamp-Lieb inequalities of Carlen and Cordero-Erausquin. As applications, we reprove a log-convexity property of the Gowers uniformity norms, and establish some reverse Lp inequalities for various tomographic transforms. We conclude with some open questions.

AB - The Brascamp-Lieb inequalities are a generalization of the Hölder, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of these inequalities, which can be viewed as an Lp version of the entropy Brascamp-Lieb inequalities of Carlen and Cordero-Erausquin. As applications, we reprove a log-convexity property of the Gowers uniformity norms, and establish some reverse Lp inequalities for various tomographic transforms. We conclude with some open questions.

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DO - 10.1112/plms.12633

M3 - Article

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Adjoint Brascamp–Lieb inequalities

Abstract

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Tomographic Fourier Analysis

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