Euclidean Forward-Reverse Brascamp-Lieb Inequalities: Finiteness,\n Structure and Extremals

2019/07/29 by Thomas A. Courtade, Jingbo Liu, Courtade, Thomas A. +1 · 5 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical Biology Tumor Growth #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1907.12723

openalex publication_date 2019/07/29 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

A new proof is given for the fact that centered gaussian functions saturate\nthe Euclidean forward-reverse Brascamp-Lieb inequalities, extending the\nBrascamp-Lieb and Barthe theorems. A duality principle for best constants is\nalso developed, which generalizes the fact that the best constants in the\nBrascamp-Lieb and Barthe inequalities are equal. Finally, as the title hints,\nthe main results concerning finiteness, structure and gaussian-extremizability\nfor the Brascamp-Lieb inequality due to Bennett, Carbery, Christ and Tao are\ngeneralized to the setting of the forward-reverse Brascamp-Lieb inequality.\n

Cited by

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• Simple and Sharp Generalization Bounds via Lifting
• Operator capacity, the Brascamp--Lieb inequality and geometric programming
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
• Multiversion of the Hausdorff--Young inequality

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