Acta mathematica scientia, Series B >
SOME SHARP RELLICH TYPE INEQUALITIES ON NILPOTENT GROUPS AND APPLICATION
Received date: 2011-10-18
Online 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).
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
LIAN Bao-Sheng . SOME SHARP RELLICH TYPE INEQUALITIES ON NILPOTENT GROUPS AND APPLICATION[J]. Acta mathematica scientia, Series B, 2013 , 33(1) : 59 -74 . DOI: 10.1016/S0252-9602(12)60194-5
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