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arXiv · 2212.11066

On the family of singular Brascamp-Lieb inequalities with dimension datum $(1, 2, 2, 1)$

Fred Yu-Hsiang Lin
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Abstract

We classify a certain family of singular Brascamp-Lieb forms which we associate with the dimension datum $(1, 2, 2, 1)$. We determine the exact range of Lebesgue exponents, for which one has singular Brascamp Lieb inequalities within this family. One key observation is a simple proof of a variant of an estimate in dyadic triangular Hilbert transform of two general and one not too general function. The remaining observations concern counter examples to boundedness. We compare with a counter example showing that the triangular Hilbert form does not satisfy singular Brascamp Lieb bounds with exponents $(\infty,p,p')$.

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Fred Yu-Hsiang Lin. 2022-12-21. On the family of singular Brascamp-Lieb inequalities with dimension datum $(1, 2, 2, 1)$. https://arxiv.org/abs/2212.11066

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