A Coercive Estimate for the Nonhomogeneous Differential Operator on the Heisenberg Group

We construct some linear nonhomogeneous differential operator $ \mathcal{Q} $ on the Heisenberg groupwhose kernel is interconnected with the Lie algebra of the group of conformal mappings.In more detail, the kernel of $ \mathcal{Q} $ coincides with first two coordinate functions of mappings ofthe Lie algebra of conformal mappings.We derive the integral representation formula andgive a coercive estimate for  $ \mathcal{Q} $ .