Weighted restriction estimates and application to Falconer distance set problem
Weighted restriction estimates and application to Falconer distance set problem
复制标题
DOI：
10.1353/ajm.2021.0005
复制
发表时间：
2018-02
影响因子：
1.7
通讯作者：
Xiumin Du;L. Guth;Yumeng Ou;Hong Wang;Bobby Wilson;Ruixiang Zhang
中科院分区：
文献类型：
--
作者：
Xiumin Du;L. Guth;Yumeng Ou;Hong Wang;Bobby Wilson;Ruixiang Zhang
摘要：我们证明了一些加权傅立叶限制估计多项式分割和改进的Schlhartz估计。作为应用，我们得到了改进的分形测度傅里叶变换的球平均衰减率，从而改进了三维及更高维空间中法尔科纳距离集猜想的结果.
abstract:We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore improve the results for the Falconer distance set conjecture in three and higher dimensions.