OPTIMAL MULTIPOLAR HARDY INEQUALITIES ON THE HEISENBERG GROUP

  • Yongyang JIN ,
  • Li TANG ,
  • Zhoutao HU ,
  • Tianqi LOU
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  • School of Mathematical Science, Zhejiang University of Technology, Hangzhou 310023, China
Yongyang JIN, E-mail: yongyang@zjut.edu.cn; Zhoutao HU, E-mail: 1023054092@qq.com; Tianqi LOU, E-mail: 1424256241@qq.com

Received date: 2025-01-08

  Revised date: 2025-07-20

  Online published: 2026-05-22

Supported by

This research was supported by the NSFC (12571108, KYY-ZX-20240230).

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.

Cite this article

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 . DOI: 10.1007/s10473-026-0213-3

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