English

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.

Keywords

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

R2 v1 2026-06-23T00:36:00.002Z