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arXiv · 1806.08051

Improved decay of conical averages of the Fourier transform

Terence L. J. Harris
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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 Schr\"odinger equation.

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Terence L. J. Harris. 2018-06-21. Improved decay of conical averages of the Fourier transform. https://doi.org/10.1090/proc/14747

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