Hardy type inequalities related to Carnot-Carathéodory distance on the Heisenberg group
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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.References
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Additional Information
- Qiao-Hua Yang
- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China
- MR Author ID: 761680
- Email: qaohyang2465@yahoo.com.cn
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 351-362
- MSC (2010): Primary 22E25; Secondary 26D10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11322-X
- MathSciNet review: 2988736