A fundamental solution for a nonelliptic partial differential operator, II

Let [Formula: see text] denote the holomorphic tangential vector field to the generalized upper-half plane [Formula: see text]. In our terminology, [Formula: see text]. Consider the [Formula: see text] operator on the boundary of [Formula: see text], [Formula: see text]; note that [Formula: see text] is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution [Formula: see text] to [Formula: see text]. Our approach is based on special functions and their properties.