论文标题
关于三线性振荡的积分不平等和相关主题
On Trilinear Oscillatory Integral Inequalities and Related Topics
论文作者
论文摘要
针对某些三线性标量值功能建立了不平等。这些功能对一个真实变量的可测量函数作用，由二维或三维空间上的集成来定义，并根据函数的Lebesgue空间规范以及描述一定程度振荡的大参数的负功率进行控制。相关的级别设置不平等是分析的核心要素。 在此草案中，主要结果和证明的主要线条在很大程度上没有变化，但是已经纠正了一些细节。该分析已经扩展了作者Durcik和Roos的工作。
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms of Lebesgue space norms of the functions, and of negative powers of large parameters describing a degree of oscillation. Related sublevel set inequalities are a central element of the analysis. The main results and the main lines of their proofs are largely unchanged in this draft, but some details have been corrected. The analysis has already been extended in work of the author, Durcik, and Roos.
