The case of equality in geometric instances of Barthe's reverse Brascamp-Lieb inequality
type: Item
instance of: scholarly article
title: The case of equality in geometric instances of Barthe's reverse Brascamp-Lieb inequality
DOI: 10.1007/978-3-031-26300-2_4
author: Károly jun. Böröczky
author: Pavlos Kalantzopoulos
author: Dongmeng Xi
publication date: 2024-09-20T00:00:00Z
review text: The Geometric Brascamp-Lieb inequality has been known in the form \N\[\N\int_{{\mathbb{R}}^n}\prod_{i=1}^kf_i(P_{E_i}x)^{c_i}dx\leq\prod_{i=1}^k\bigg(\int_{E_i}f_i\bigg)^{c_i}\N\]\Nfor subspaces \(E_1,\dots, E_k\) of \({\mathbb{R}}^n\) and \(c_1, \dots, c_k>0\) satisfying the Geometric Brascamp-Lieb data relation \N\[\N\sum_{i=1}^kc_iP_{E_i}=I_n,\N\]\Nafter the works of Brascamp-Lieb, Ball, Barthe et al. The extremals \(f_i, i=1,2,\dots, k\) for which the equality of Geometric Brascamp-Lieb inequality holds were classified later by Valdimarsson. In this paper, the authors classify the extremals for which the Barthe's reverse Geometric Brascamp-Lieb inequality \N\[\N\int^*_{{\mathbb{R}}^n}\sup_{x=\sum\limits_{i=1}^kc_ix_i,\ x_i\in E_i}\prod_{i=1}^kf_i(x_i)^{c_i}dx\geq\prod_{i=1}^k\bigg(\int_{E_i}f_i\bigg)^{c_i}\N\]\Nholds with equality.\N\NFor the entire collection see [Zbl 1527.46003].
reviewed by: Shi-Zhong Du
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 7916418
zbMATH Keywords: Brascamp-Lieb inequality
zbMATH Keywords: reverse geometric Brascamp-Lieb inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7916418