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arXiv · 2608.17952

Mixed-norm Brascamp-Lieb inequalities

Ruixiang Zhang
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Abstract

Christ [Chr01] looked at a certain boundedness problem for trilinear operators. In this paper we set up a framework of mixed-norm Brascamp-Lieb inequalities and identify a new interesting regime not covered by the study of classical Brascamp-Lieb. Positive results in [Chr01] can be viewed as the first nontrivial progress in this new regime. We will also prove another mixed-norm Brascamp-Lieb inequality, showcasing how one can use a tensor product trick to slightly sharpen Christ's argument and also obtain the endpoint case. We then discuss the connections between mixed-norm Brascamp-Lieb and the Kakeya Conjectures, as well as unique new difficulties for these mixed-norm Brascamp-Lieb inequalities compared to the classical setting.

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Ruixiang Zhang. 2026-08-18. Mixed-norm Brascamp-Lieb inequalities. https://arxiv.org/abs/2608.17952

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