调和分析中的高阶横截性
Higher order transversality in harmonic analysis
摘要：
在微分拓扑中，称欧几里得空间的两个光滑子流形$S_1$和$S_2$是横截的，如果在每个公共点处的切空间一起形成一个生成集。这篇文章的目的是探讨一个更一般的概念横截性有关的一个收集的子流形的欧几里得空间。特别是，我们表明，三个看似不同的概念自然产生的横向调和分析，实际上是等价的。这一结果是一个合并的几个最近的作品的变种Brascamp-Lieb不等式，我们借此机会在这里简要地调查这一不断增长的领域。这并不是一个详尽的叙述，所作的选择反映了作者的特殊观点。
英文摘要：
In differential topology two smooth submanifolds $S_1$ and $S_2$ of euclidean space are said to be transverse if the tangent spaces at each common point together form a spanning set. The purpose of this article is to explore a much more general notion of transversality pertaining to a collection of submanifolds of euclidean space. In particular, we show that three seemingly different concepts of transversality arising naturally in harmonic analysis, are in fact equivalent. This result is an amalgamation of several recent works on variants of the Brascamp--Lieb inequality, and we take the opportunity here to briefly survey this growing area. This is not intended to be an exhaustive account, and the choices made reflect the particular perspectives of the authors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
