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arXiv · 1802.10186

Weighted restriction estimates and application to Falconer distance set problem

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

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Xiumin Du, Larry Guth, Yumeng Ou, Hong Wang, Bobby Wilson, Ruixiang Zhang. 2018-02-27. Weighted restriction estimates and application to Falconer distance set problem. https://arxiv.org/abs/1802.10186

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