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) |
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Pages (from-to) | 175-211 |
Number of pages | 37 |
Journal | American Journal of Mathematics |
Volume | 143 |
Issue number | 1 |
DOIs | |
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