Improved decay of conical averages of the Fourier transform
Analysis of PDEs
2019-11-05 v4 Classical Analysis and ODEs
Abstract
An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension . 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.
Keywords
Cite
@article{arxiv.1806.08051,
title = {Improved decay of conical averages of the Fourier transform},
author = {Terence L. J. Harris},
journal= {arXiv preprint arXiv:1806.08051},
year = {2019}
}
Comments
15 pages. Accepted version