Weighted restriction estimates and application to Falconer distance set problem | Zendy

Xiumin Du | Zendy; Larry Guth | Zendy; Yumeng Ou | Zendy; Hong Wang | Zendy; Bobby Wilson | Zendy; Ruixiang Zhang | Zendy

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Weighted restriction estimates and application to Falconer distance set problem

Author(s) -

Xiumin Du,

Larry Guth,

Yumeng Ou,

Hong Wang,

Bobby Wilson,

Ruixiang Zhang

Publication year - 2021

Publication title -

american journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.818

H-Index - 67

eISSN - 1080-6377

pISSN - 0002-9327

DOI - 10.1353/ajm.2021.0005

Subject(s) - mathematics , conjecture , fourier transform , set (abstract data type) , fractal , polynomial , mathematical analysis , combinatorics , algorithm , computer science , programming language

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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