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

 

Hardy type inequalities related to Carnot-Carathéodory distance on the Heisenberg group


Author: Qiao-Hua Yang
Journal: Proc. Amer. Math. Soc. 141 (2013), 351-362
MSC (2010): Primary 22E25; Secondary 26D10
Published electronically: May 17, 2012
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Abstract: Being motivated by a representation formula associated with the Korányi-Folland nonisotropic gauge proved by Cohn and Lu, we prove an analogous representation formula related to the Carnot-Carathéodory distance on the Heisenberg group. Using this formula, we obtain some Hardy inequalities associated with the Carnot-Carathéodory distance on such groups.


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Additional Information

Qiao-Hua Yang
Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China
Email: qaohyang2465@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11322-X
PII: S 0002-9939(2012)11322-X
Keywords: Hardy inequalities, Heisenberg group, Carnot-Carathéodory distance
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: September 2, 2010, and June 14, 2011
Published electronically: May 17, 2012
Additional Notes: This work was supported by the National Science Foundation of China under Grant No. 10671009.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.