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

 

A note on the cone restriction conjecture


Authors: Changxing Miao, Junyong Zhang and Jiqiang Zheng
Journal: Proc. Amer. Math. Soc. 140 (2012), 2091-2102
MSC (2010): Primary 35Q40, 35Q55, 47J35
Published electronically: October 20, 2011
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Abstract: This paper is devoted to the study of the restriction problem in harmonic analysis. Based on the spherical harmonics expansion and analyzing the asymptotic behavior of the Bessel function, we show that a modified linear adjoint restriction estimate holds for all Schwartz functions compactly supported on the cone, which generalizes Shao's result.


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Additional Information

Changxing Miao
Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, People’s Republic of China 100088
Email: miao_changxing@iapcm.ac.cn

Junyong Zhang
Affiliation: The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing, People’s Republic of China 100088
Address at time of publication: Department of Mathematics, Beijing Institute of Technology, Beijing, People’s Republic of China 100081 – and – Beijing Computational Science Research, Beijing, People’s Republic of China 100084
Email: zhangjunyong111@sohu.com

Jiqiang Zheng
Affiliation: The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing, People’s Republic of China 100088
Email: zhengjiqiang@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11076-1
PII: S 0002-9939(2011)11076-1
Keywords: Linear adjoint restriction estimate, spherical harmonics
Received by editor(s): September 15, 2010
Received by editor(s) in revised form: January 18, 2011, and February 11, 2011
Published electronically: October 20, 2011
Communicated by: Hart F. Smith
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.