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arXiv · 2112.15101

Local bounds for singular Brascamp-Lieb forms with cubical structure

Polona Durcik·Lenka Slavíková·Christoph Thiele
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Abstract

We prove a range of $L^p$ bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We allow $2^{m-1}<p\le \infty$ with $m$ the dimension of the cube, extending an earlier result that required $p=2^m$. The threshold $2^{m-1}$ is sharp in our theorems.

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Polona Durcik, Lenka Slavíková, Christoph Thiele. 2021-12-30. Local bounds for singular Brascamp-Lieb forms with cubical structure. https://arxiv.org/abs/2112.15101

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