Weighted restriction estimates and application to falconer distance set problem

Xiumin Du, Larry Guth, Yumeng Ou, Hong Wang, Bobby Wilson, Ruixiang Zhang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)175-211
Number of pages37
JournalAmerican Journal of Mathematics
Volume143
Issue number1
DOIs
StatePublished - Feb 2021

ASJC Scopus subject areas

  • Mathematics(all)

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