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arXiv · 2610.34289

Remarks on the Brascamp--Lieb inequality

Dario Cordero-Erausquin·Galyna V. Livshyts·Liran Rotem
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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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Dario Cordero-Erausquin, Galyna V. Livshyts, Liran Rotem. 2026-10-25. Remarks on the Brascamp--Lieb inequality. https://arxiv.org/abs/2610.34289

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