论文标题
关于精致的Strichartz估计和最大扩展操作员的注释
A note on the refined Strichartz estimates and maximal extension operator
论文作者
论文摘要
本文有两个部分。在第一部分中，我们将DU，Guth，Li和Zhang的最新论文扩展到更一般的相位功能。主要方法是Bourgain-Demeter的$ l^2 $解耦定理并在尺度上诱导。在第二部分中，我们证明了具有正主曲率阳性曲面的最大扩展算子的一些积极结果。主要方法是Du和Zhang的尖锐$ l^2 $估计，以及Wolff和Tao的Birinear方法。
There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to a more general class of phase functions. The main methods are Bourgain-Demeter's $l^2$ decoupling theorem and induction on scales. In the second part, we prove some positive results for the maximal extension operator for hypersurfaces with positive principal curvatures. The main methods are sharp $L^2$ estimates by Du and Zhang, and the bilinear method by Wolff and Tao.
