Weighted restriction estimates and application to Falconer distance set problem
Classical Analysis and ODEs
2018-03-01 v1
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.
Cite
@article{arxiv.1802.10186,
title = {Weighted restriction estimates and application to Falconer distance set problem},
author = {Xiumin Du and Larry Guth and Yumeng Ou and Hong Wang and Bobby Wilson and Ruixiang Zhang},
journal= {arXiv preprint arXiv:1802.10186},
year = {2018}
}
Comments
26 pages