A remark on circular means of Fourier transforms of measures

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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.
The proof of the main result in this paper is incorrect, and this paper has been withdrawn

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Classical Analysis and ODEs, 42B10, 28A75

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http://salesiana.dossiersoluciones.com/handle/123456789/58493

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0001030
 http://arxiv.org/abs/math/0001030

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arXiv