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arXiv 1401.0467math.CA
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关于经典分数次奇异积分能量反演失败的一个注记

A note on failure of energy reversal for classical fractional singular integrals

Eric T. Sawyer, Chun-Yen Shen, Ignacio Uriarte-Tuero

备注：
24 pages. This version references a correct form of the T1 theorem, corrects typos and uses Bochner's theorem to complete the proof for the missing range of alpha, and also points out an easy extension to higher dimensions. arXiv admin note: text overlap with arXiv:1305.5104
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摘要：

对于[0，n）中的α，我们证明了α-分数阶里斯变换向量的能量反转失败，更一般地，对于任何在球面的每个大圆上具有零积分核的α-分数阶卷积奇异积分向量的能量反转失败.

英文摘要：

For alpha in [0,n) we demonstrate the failure of energy reversal for the vector of alpha-fractional Riesz transforms, and more generally for any vector of alpha-fractional convolution singular integrals having a kernel with vanishing integral on every great circle of the sphere.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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