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Weighted restriction estimates and application to Falconer distance set problem
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 1, February 2021
- pp. 175-211
- 10.1353/ajm.2021.0005
- Article
- Additional Information
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.