  We establish a Liouville-type theorem for a subcritical nonlinear problem,
involving a fractional power of the sub-Laplacian in the Heisenberg group. To
prove our result we will use the local realization of fractional CR covariant
operators, which can be constructed as the Dirichlet-to-Neumann operator of a
degenerate elliptic equation in the spirit of Caffarelli and Silvestre, as
established in \cite{FGMT}. The main tools in our proof are the CR inversion
and the moving plane method, applied to the solution of the lifted problem in
the half-space $\mathbb H^n\times \mathbbR^+$.

Analysis of PDEs