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

Abstract

We construct some linear nonhomogeneous differential operator \( \mathcal{Q} \) on the Heisenberg group whose 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 of the Lie algebra of conformal mappings. We derive the integral representation formula and give a coercive estimate for \( \mathcal{Q} \).