Weighted restriction estimates and application to Falconer distance set problem

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.

26 pages

References in corpus (1)

• A cone restriction estimate using polynomial partitioning

Cited by in corpus (16)

• Configuration sets with nonempty interior
• On Falconer's distance set problem in the plane
• Improved decay of conical averages of the Fourier transform
• Upper bounds for Fourier decay rates of fractal measures
• Microlocal decoupling inequalities and the distance problem on Riemannian manifolds
• Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates
• Hausdorff dimension of pinned distance sets and the $L^2$-method
• Fourier restriction in low fractal dimensions
• An improved dimensional threshold for the angle problem
• Finite Point Configurations and the Regular Value Theorem in a Fractal setting
• Tomography bounds for the Fourier extension operator and applications
• Refined Strichartz inequalities for the wave equation
• Distribution of determinant of sum of matrices
• $L^2$ Schrödinger maximal estimates associated with finite type phases in ${\mathbb{R}}^2$
• Incidence estimates for well spaced tubes
• A Mattila-Sjölin theorem for triangles