Optimal multipolar Hardy inequalities on the Heisenberg group
摘要
Based on the left-invariant property of the standard vector fields, we prove a class of one-parameter multipolar Hardy inequalities on the Heisenberg group by the method of super-solutions. Furthermore, we obtain the criticality of the corresponding Schrödinger operators in certain parameter range by constructing suitable sequence of minimization functions, which means that we have got some optimal multipolar Hardy inequalities on the Heisenberg group. The attainability of the sharp constant is also considered, unlike the case of unipolar classical Hardy inequality, the sharp constant is attained for certain parameter range in the multipolar case.