English

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 d4d \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.

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