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.

15 pages. Accepted version