Research Article
Symmetry of Solutions of Integral Equation in the Heisenberg Group
Zhaobing Cui
,
Wei Shi*
Issue:
Volume 15, Issue 2, April 2026
Pages:
11-17
Received:
11 February 2026
Accepted:
25 February 2026
Published:
18 March 2026
DOI:
10.11648/j.pamj.20261502.11
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Abstract: This paper investigates the existence and symmetry properties of solutions to a class of integral equations on the Heisenberg group. Building upon the moving plane method and Hardy-Littlewood-Sobolev type inequalities, we establish symmetry and monotonicity results for positive solutions of the integral equation. This paper extends classical Euclidean results to the Heisenberg group, highlighting profound interactions between geometry and analysis.
Abstract: This paper investigates the existence and symmetry properties of solutions to a class of integral equations on the Heisenberg group. Building upon the moving plane method and Hardy-Littlewood-Sobolev type inequalities, we establish symmetry and monotonicity results for positive solutions of the integral equation. This paper extends classical Euclid...
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