Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (1): 59-74.doi: 10.1016/S0252-9602(12)60194-5

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SOME SHARP RELLICH TYPE INEQUALITIES ON NILPOTENT GROUPS AND APPLICATION

 LIAN Bao-Sheng   

  1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
  • Received:2011-10-18 Online:2013-01-20 Published:2013-01-20
  • Supported by:

    Supported by National Science Foundation of China (10901126); Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Y201106); National Science Founda-tion of Hubei Province (2010CDB03305); Wuhan Chenguang Process (201150431096); Open Fund of State Key Lab of Information Engineering in Surveying Mapping and Remote Sensing (11R01).

Abstract:

We prove some Rellich type inequalities for the sub-Laplacian on Carnot nilpotent groups. Using the same method, we obtain some analogous inequalities for the Heisenberg-Greiner operators. In most cases, the constants we obtained are optimal.

Key words: Rellich inequality, Carnot group, Heisenberg-Greiner operators

CLC Number: 

  • 35H10
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