Improved decay of conical averages of the Fourier transform

Harris, Terence

doi:10.1090/proc/14747

Improved decay of conical averages of the Fourier transform
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by Terence L. J. Harris PDF

Proc. Amer. Math. Soc. 147 (2019), 4781-4796 Request permission

Abstract:

An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d \geq 4$. 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.

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