论文标题
谐波分析中的高阶横向性
Higher order transversality in harmonic analysis
论文作者
论文摘要
在差异拓扑中，如果每个公共点的切线空间一起形成一个跨度集，则据说两个平滑的子手机$ s_1 $和$ s_2 $的欧几里得空间是横向的。本文的目的是探讨与欧几里得空间的子曼群集合有关的更一般的横向概念。特别是，我们表明，在谐波分析中自然产生的三个看似不同的横向概念实际上是等效的。该结果是对Brascamp- lieb不平等变异的最近几部作品的合并，我们借此机会简要调查了这一增长区域。这并不是要详尽的说明，而做出的选择反映了作者的特定观点。
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.
