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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 restriction theorem for the H-type groups


Authors: Heping Liu and Yingzhan Wang
Journal: Proc. Amer. Math. Soc. 139 (2011), 2713-2720
MSC (2010): Primary 42B10, 43A65
Published electronically: March 22, 2011
MathSciNet review: 2801610
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Abstract: We prove that the restriction operator for the H-type groups is bounded from $ L^p$ to $ L^{p'}$ for $ p$ near to $ 1$ when the dimension of the center is larger than one, and the range of $ p$ depends on the dimension of the center. This is different from the Heisenberg group, on which the restriction operator is not bounded from $ L^p$ to $ L^{p'}$ unless $ p=1$.


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Additional Information

Heping Liu
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: hpliu@pku.edu.cn

Yingzhan Wang
Affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, People’s Republic of China
Email: wyzde@tom.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10907-9
Keywords: H-type group, restriction operator, special Hermite expansion
Received by editor(s): May 12, 2010
Published electronically: March 22, 2011
Additional Notes: The authors were supported by the National Natural Science Foundation of China under Grants #10871003 and #10990012, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant #2007001040.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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