Upper bounds for Fourier decay rates of fractal measures

Abstract

For spherical and parabolic averages of the Fourier transform of fractal measures, we obtain new upper bounds on rates of decay by an "intermediate dimension" trick.

arXiv comment19 pages

References in corpus (3)

• Weighted restriction estimates and application to Falconer distance set problem
• An $L^2$-identity and pinned distance problem
• Pointwise convergence of the fractional Schrödinger equation in ${\mathbb{R}}^2$

Cited by in corpus (5)

• An improved result for Falconer's distance set problem in even dimensions
• Pointwise convergence over fractals for dispersive equations with homogeneous symbol
• Counterexamples for the fractal Schrödinger convergence problem with an intermediate space trick
• Convergence over fractals for the Schrödinger equation
• Dimension of divergence set of the wave equation