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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

Yingzhan Wang
Affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, People’s Republic of China

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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