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A Hardy inequality with remainder terms in the Heisenberg group and the weighted eigenvalue problem. (English) Zbl 1133.26019
Summary: 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 p-sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
MSC:
26D15Inequalities for sums, series and integrals of real functions
43A80Analysis on other specific Lie groups
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