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A remark on circular means of Fourier transforms of measures

Terence Tao
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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.

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Terence Tao. 2000-07-11. A remark on circular means of Fourier transforms of measures. https://arxiv.org/abs/math/0001030

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