@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 = "Funding Information: 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. {\textcopyright} 2021 by Johns Hopkins University Press. 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",
}