Weighted restriction estimates and application to falconer distance set problem

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

doi:10.1353/ajm.2021.0005

Weighted restriction estimates and application to falconer distance set problem

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	175-211
Number of pages	37
Journal	American Journal of Mathematics
Volume	143
Issue number	1
DOIs	https://doi.org/10.1353/ajm.2021.0005
State	Published - Feb 2021

ASJC Scopus subject areas

General Mathematics

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title = "Weighted restriction estimates and application to falconer distance set problem",

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.",

author = "Xiumin Du and Larry Guth and Yumeng Ou and Hong Wang and Bobby Wilson and Ruixiang Zhang",

note = "Publisher Copyright: {\textcopyright} 2021 by Johns Hopkins University Press.",

year = "2021",

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doi = "10.1353/ajm.2021.0005",

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AU - Du, Xiumin

AU - Guth, Larry

AU - Ou, Yumeng

AU - Wang, Hong

AU - Wilson, Bobby

AU - Zhang, Ruixiang

PY - 2021/2

Y1 - 2021/2

N2 - 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.

AB - 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.

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EP - 211

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 1

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Weighted restriction estimates and application to falconer distance set problem

Abstract

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