论文标题
Brascamp-Lieb类型的五线性单数积分估计值
Five-Linear Singular Integral Estimates of Brascamp-Lieb Type
论文作者
论文摘要
我们证明了Brascamp-Lieb类型的五线性单数积分的全部估计值。这项研究以方法为导向，目的是开发一种足够通用的技术来估计不遵守Hölder缩放的Brascamp-Lieb不平等现象的奇异积分变体。发明的方法从较低维度的子空间的本地信息中构建了整个空间的局部分析，并将此类张量型参数与通用局部分析相结合。五线性单数积分的界限的直接结果是莱布尼兹规则，它捕获了从横向方向的波的非线性相互作用。
We prove the full range of estimates for a five-linear singular integral of Brascamp-Lieb type. The study is methodology-oriented with the goal to develop a sufficiently general technique to estimate singular integral variants of Brascamp-Lieb inequalities that do not obey Hölder scaling. The invented methodology constructs localized analysis on the entire space from local information on its subspaces of lower dimensions and combines such tensor-type arguments with the generic localized analysis. A direct consequence of the boundedness of the five-linear singular integral is a Leibniz rule which captures nonlinear interactions of waves from transversal directions.
