Improved decay of conical averages of the Fourier transform

Abstract

An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d\ge 4$. The proof uses a weighted version of the broad restriction inequality, a narrow decoupling inequality for the cone, and some techniques of Du and Zhang originally developed for the Schrödinger equation.

arXiv comment15 pages. Accepted version

References in corpus (4)

• Weighted restriction estimates and application to Falconer distance set problem
• An $L^2$-identity and pinned distance problem
• A cone restriction estimate using polynomial partitioning
• Fractal Strichartz estimate for the wave equation

Cited by in corpus (7)

• On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data
• Improved local smoothing estimate for the wave equation in higher dimensions
• $L^p-L^q$ local smoothing estimates for the wave equation via $k$-broad Fourier restriction
• Circular average relative to fractal measures
• Improved bounds for restricted projection families via weighted Fourier restriction
• Fourier restriction in low fractal dimensions
• Fourier decay of fractal measures on surfaces of co-dimension two in ${\mathbb{R}}^5$