A remark on circular means of Fourier transforms of measures
Terence Tao
Abstract
In a recent paper of Wolff the optimal decay of circular Lp 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.
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