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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fourier spectrum characterization of Hardy spaces and applications


Authors: Tao Qian, Yuesheng Xu, Dunyan Yan, Lixin Yan and Bo Yu
Journal: Proc. Amer. Math. Soc. 137 (2009), 971-980
MSC (2000): Primary 42A38
Published electronically: September 11, 2008
MathSciNet review: 2457437
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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize in terms of Fourier spectrum the boundary values of functions in the complex Hardy spaces $ H^p(\mathbb{C}_\pm), 1\leq p\leq \infty.$ As an application we extend the Bedrosian identity, originally stated for square-integrable functions, to the $ L^{p}(\mathbb{R})$ cases.


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Additional Information

Tao Qian
Affiliation: Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, China SAR
Email: fsttq@umac.mo

Yuesheng Xu
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 12344
Email: yxu06@syr.edu

Dunyan Yan
Affiliation: School of Information Science and Engineering, The Graduate University of the Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: ydunyan@gucas.ac.cn

Lixin Yan
Affiliation: Department of Mathematics, Zhongshan University, Guangzhou 510275, People’s Republic of China
Email: mcsylx@mail.sysu.edu.cn

Bo Yu
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China
Email: yubo2003@amss.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09544-0
PII: S 0002-9939(08)09544-0
Received by editor(s): September 20, 2007
Received by editor(s) in revised form: February 24, 2008
Published electronically: September 11, 2008
Additional Notes: The first author was supported by a research grant from the University of Macau, No. RG079/04-05S/QT/FST, and by the Macao Science and Technology Development Fund 051/2005/A
The second author was supported in part by the U.S. National Science Foundation under grant CCR-0407476, by the Natural Science Foundation of China under grant 10371122, and by the Ministry of Education of the People’s Republic of China under the Changjiang Scholar Chair Professorship program
The third author was supported by the Presidential Foundation of the Graduate School of the Chinese Academy of Sciences (yzjj200505) and NSF of China (10571014 and 10631068)
The fourth author was supported by the NSF of China (Grant No. 10371134/11571082 and 10571014/10631080)
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society