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中国科学院大学学报 ›› 2017, Vol. 34 ›› Issue (6): 657-659.DOI: 10.7523/j.issn.2095-6134.2017.06.001

• 数学与物理学 •    下一篇

D(Rn)函数的Riesz变换的一个注记

魏明权1,2, 沈峰2, 燕敦验2   

  1. 1. 信阳师范学院数学与统计学院, 河南 信阳 464000;
    2. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2016-06-08 修回日期:2016-07-13 发布日期:2017-11-15
  • 通讯作者: 燕敦验
  • 基金资助:
    Supported by the National Nature Science Foundation of China (11471309, 11271162, and 11561062), and Project of Henan Provincial Department of Education(18A110028)

A note of Riesz transform on D(Rn)

WEI Mingquan1,2, SHEN Feng2, YAN Dunyan2   

  1. 1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2016-06-08 Revised:2016-07-13 Published:2017-11-15
  • Supported by:
    Supported by the National Nature Science Foundation of China (11471309, 11271162, and 11561062), and Project of Henan Provincial Department of Education(18A110028)

摘要: 证明,对于任意一个非零D(Rn)函数f,它的Riesz变换Rjf不具有紧支集。这推广了已知的Hilbert变换的结果。

关键词: Riesz变换, D(Rn), 紧支集

Abstract: In this work, we prove that, for a non-zero function fD(Rn), its Riesz transform Rjf does not have compact support, which improves the known result of Hilbert transform.

Key words: Riesz transform, D(Rn), compact support

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