The CR fractional Laplacian and the fractional CR Yamabe problem

The boundary of the complex hyperbolic space may be identified with the usual Heisenberg group; this is a particular example of a Kahler-Einstein manifold having a CR manifold as boundary. We will consider the construction of the CR fractional Laplacian through an extension problem, in the same spirit as the Caffarelli-Silvestre exension for the real case. This allows to set up a fractional CR Yamabe problem.