Weighted restriction estimates and application to Falconer distance set problem
Xiumin Du, Larry Guth, Yumeng Ou, Hong Wang, Bobby Wilson, Ruixiang Zhang
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.
Topics & Concepts
MathematicsConjectureFourier transformSet (abstract data type)FractalPolynomialMathematical analysisCombinatoricsAlgorithmComputer scienceProgramming languageMathematical Dynamics and Fractalsadvanced mathematical theoriesMathematical Analysis and Transform Methods