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

31 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 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

Funding

Manuscript received March 8, 2018; revised July 11, 2018. Research of the first author supported by the National Science Foundation under Grant No. 1638352 and the Shiing-Shen Chern Fund; research of the second author supported by a Simons Investigator Award; research of the third author supported by the National Science Foundation DMS #1764454; research of the sixth author supported by the National Science Foundation under Grant No. 1638352 and the James D. Wolfensohn Fund. American Journal of Mathematics 143 (2021), 175–211. © 2021 by Johns Hopkins University Press.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1353/ajm.2021.0005

Cite this

@article{8bb2daa49c4445469edec05310547a21,

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",

month = feb,

doi = "10.1353/ajm.2021.0005",

language = "English (US)",

volume = "143",

pages = "175--211",

journal = "American Journal of Mathematics",

issn = "0002-9327",

publisher = "Johns Hopkins University Press",

number = "1",

}

TY - JOUR

T1 - Weighted restriction estimates and application to falconer distance set problem

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.

UR - http://www.scopus.com/inward/record.url?scp=85100040072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85100040072&partnerID=8YFLogxK

U2 - 10.1353/ajm.2021.0005

DO - 10.1353/ajm.2021.0005

M3 - Article

AN - SCOPUS:85100040072

SN - 0002-9327

VL - 143

SP - 175

EP - 211

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 1

ER -

Weighted restriction estimates and application to falconer distance set problem

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this