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Remarks on the Brascamp--Lieb inequality
Abstract
We prove several variants of the Brascamp--Lieb inequality which are adapted to additional symmetries, weights, and non-Euclidean radial structures. First, an improved Brascamp--Lieb inequality for even functions yields a strengthened Prékopa--Leindler theorem for even strongly log-concave functions. We also record a Legendre-transform proof of a generalized log-Sobolev inequality for log-concave functions. Further results include a Brascamp--Lieb inequality with a concave weight, an unconditional second-order Poincaré inequality, a rotation-trick improvement for arbitrary even log-concave measures, and a Poincaré-type inequality associated with smooth norms.
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BibTeX
@misc{corderoerausquin2026remarks,
title = {{Remarks on the Brascamp--Lieb inequality}},
author = {Dario Cordero-Erausquin and Galyna V. Livshyts and Liran Rotem},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34289},
eprint = {2610.34289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34289},
}
RIS
TY - UNPB
TI - Remarks on the Brascamp--Lieb inequality
AU - Dario Cordero-Erausquin
AU - Galyna V. Livshyts
AU - Liran Rotem
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34289
UR - https://arxiv.org/abs/2610.34289
AB - We prove several variants of the Brascamp--Lieb inequality which are adapted to additional symmetries, weights, and non-Euclidean radial structures. First, an improved Brascamp--Lieb inequality for even functions yields a strengthened Prékopa--Leindler theorem for even strongly log-concave functions. We also record a Legendre-transform proof of a generalized log-Sobolev inequality for log-concave functions. Further results include a Brascamp--Lieb inequality with a concave weight, an unconditional second-order Poincaré inequality, a rotation-trick improvement for arbitrary even log-concave measures, and a Poincaré-type inequality associated with smooth norms.
ER -