关于维数为（1,2,2,1）的奇异Brascamp-Lieb不等式族

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-12-08 DOI:10.1112/mtk.70003

Fred Yu-Hsiang Lin

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引用次数: 0

摘要

在三角形希尔伯特变换的激励下，我们分类了一类奇异的Brascamp-Lieb形式，并将其与维数（1,2,2,1）联系起来。我们确定了Lebesgue指数的确切范围，其中一个在这个家族中具有奇异的Brascamp-Lieb不等式。其余的观察涉及有界性的反例。通过与反例的比较，证明了三角形Hilbert形式在端点上不满足奇异Brascamp-Lieb界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

Motivated by the triangular Hilbert transform, 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. 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 in the endpoints.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.