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| 摘要: |
| 设E是R中一可测子集，H为Hilbert变换.本文研究了H（χE）的Lp积分及其分布函数的相关性质.利用初等但精细的分析，给出了上述积分和分布函数的具体表达式.本文所采用的方法给出了文献[6]中结果的一个新的证明. |
| 关键词: Hilbert变换 分布函数 Lp范数 |
| DOI： |
| 分类号:O174.1 |
| 基金项目:Supported by National Natual Science Foundation of China(11471033); Anhui Provincial Natural Science Foundation (1408085MA01); University NSR Project of Anhui Province (KJ2014A087). |
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| A NOTE ON HILBERT TRANSFORM OF A CHARACTERISTIC FUNCTION |
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QU Meng,JIANG Man-ru
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| Abstract: |
| Let E be a measurable subset in R and H be the Hilbert transform. In this paper, we study some properties on the Lp integral and distribution function of H(χE). Based on elementary and accurate analysis, exact formulas are given for the above integral an distribution function. Our method adopted here gives a new proof of the results in[6]. |
| Key words: Hilbert transform distribution function Lp norm |
