D(Rn)函数的Riesz变换的一个注记

魏明权; 沈峰; 燕敦验

doi:10.7523/j.issn.2095-6134.2017.06.001

中国科学院大学学报 >

2017 , Vol. 34 >Issue 6: 657 - 659

DOI: https://doi.org/10.7523/j.issn.2095-6134.2017.06.001

数学与物理学

D(Rⁿ)函数的Riesz变换的一个注记

魏明权 ,
沈峰 ,
燕敦验

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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

网络出版日期: 2017-11-15

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)

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A note of Riesz transform on D(Rⁿ)

WEI Mingquan ,
SHEN Feng ,
YAN Dunyan

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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 date: 2016-06-08

Revised date: 2016-07-13

Online 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)

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摘要

证明，对于任意一个非零D（Rⁿ）函数f，它的Riesz变换R_jf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

本文引用格式

魏明权 , 沈峰 , 燕敦验 . D(Rⁿ)函数的Riesz变换的一个注记[J]. 中国科学院大学学报, 2017 , 34(6) : 657 -659 . DOI: 10.7523/j.issn.2095-6134.2017.06.001

Abstract

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

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

参考文献

[1] Grafakos L. Classical and modern Fourier analysis[M]. New Jersey:Pearson Education Inc, 2004.
[2] Yang L. A distribution space for Hilbert transform and its applications[J]. Science in China Series A:Mathematics, 2008, 51(12):2217-2230.
[3] Cui X, Wang R, Yan D. Some properties for double Hilbert transform on D(R²)[J]. Frontiers of Mathematics in China, 2013, 8(4):783-799.
[4] Shen F. High-dimensional Hilbert transform on D(Rⁿ)[D]. Beijing:University of Chinese Academy of Sciences, 2014(in Chinese).
[5] Royden H L, Fitzpatrick P. Real analysis[M]. New York:Macmillan, 1988.

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