A note of Riesz transform on D(Rn)

WEI Mingquan; SHEN Feng; YAN Dunyan

doi:10.7523/j.issn.2095-6134.2017.06.001

Journal of University of Chinese Academy of Sciences >

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

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

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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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

Cite this article

WEI Mingquan , SHEN Feng , YAN Dunyan . A note of Riesz transform on D(Rⁿ)[J]. Journal of University of Chinese Academy of Sciences, 2017 , 34(6) : 657 -659 . DOI: 10.7523/j.issn.2095-6134.2017.06.001

References

[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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