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.
Cui et al. (Wed,) studied this question.