Adjoint Brascamp-Lieb inequalities

Jonathan Bennett; Terence Tao

doi:10.48550/arXiv.2306.16558

Adjoint Brascamp-Lieb inequalities

Jonathan Bennett, Terence Tao

Mathematics

Research output: Working paper/Preprint › Preprint

27 Downloads (Pure)

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 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.

Original language	English
Publisher	arXiv
Pages	1-43
Number of pages	43
DOIs	https://doi.org/10.48550/arXiv.2306.16558
Publication status	Published - 28 Jun 2023

Bibliographical note

43 pages; some further references and remarks added

Keywords

math.CA
math.FA
44A12, 11B30

Access to Document

10.48550/arXiv.2306.16558Licence: Creative Commons: Attribution (CC BY)

2306.16558v2Final published version, 465 KBLicence: Creative Commons: Attribution (CC BY)

Cite this

@techreport{5cb758a9866b45db9b5b88c6e7ef3c4c,

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.",

keywords = "math.CA, math.FA, 44A12, 11B30",

author = "Jonathan Bennett and Terence Tao",

note = "43 pages; some further references and remarks added",

year = "2023",

month = jun,

day = "28",

doi = "10.48550/arXiv.2306.16558",

language = "English",

pages = "1--43",

publisher = "arXiv",

type = "WorkingPaper",

institution = "arXiv",

}

TY - UNPB

T1 - Adjoint Brascamp-Lieb inequalities

AU - Bennett, Jonathan

AU - Tao, Terence

N1 - 43 pages; some further references and remarks added

PY - 2023/6/28

Y1 - 2023/6/28

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.

KW - math.CA

KW - math.FA

KW - 44A12, 11B30

U2 - 10.48550/arXiv.2306.16558

DO - 10.48550/arXiv.2306.16558

M3 - Preprint

SP - 1

EP - 43

BT - Adjoint Brascamp-Lieb inequalities

PB - arXiv

ER -

Adjoint Brascamp-Lieb inequalities

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this