A remark on circular means of Fourier transforms of measures
Classical Analysis and ODEs
2007-05-23 v2
Abstract
In a recent paper of Wolff the optimal decay of circular L^p means of compactly supported measures of finite energy was given for p>=2, with application to Falconer's distance problem. The question was then raised in that paper as to whether any non-trivial improvement to these estimates were available for p < 2. We answer this question in the negative.
Keywords
Cite
@article{arxiv.math/0001030,
title = {A remark on circular means of Fourier transforms of measures},
author = {Terence Tao},
journal= {arXiv preprint arXiv:math/0001030},
year = {2007}
}
Comments
The proof of the main result in this paper is incorrect, and this paper has been withdrawn