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  • Research Article
  • Open Access

A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem

Journal of Inequalities and Applications20072007:032585

  • Received: 22 March 2007
  • Accepted: 20 October 2007
  • Published:


Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the -sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.


  • Vector Field
  • Asymptotic Behaviour
  • Eigenvalue Problem
  • Sobolev Space
  • Heisenberg Group


Authors’ Affiliations

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China


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© Jingbo Dou et al. 2007

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