OPTIMAL MULTIPOLAR HARDY INEQUALITIES ON THE HEISENBERG GROUP

doi:10.1007/s10473-026-0213-3

Abstract

Abstract: 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.

Key words: Hardy type inequalities, multipolar Hardy inequalities, Heisenberg group

CLC Number:

42B37

Yongyang JIN, Li TANG, Zhoutao HU, Tianqi LOU. OPTIMAL MULTIPOLAR HARDY INEQUALITIES ON THE HEISENBERG GROUP[J].Acta mathematica scientia,Series B, 2026, 46(2): 767-780.

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