A CLASS OF HOMOGENEOUS LEFT INVARIANT OPERATORS ON THE NILPOTENT LIE GROUP-G(D+2)

This paper is devoted to a class of homogeneous left invariant operato rs L(lambda) on the nilpotent Lie group G(d+2) of the form [GRAPHICS] where {X1, ..., X(d), T1, T2} is a base of left invariant VeCtor field s on G(d+2). With aid of harmonic analysis on nilpotent Lie groups and the method of increment operators, for all admissible L(lambda), sube lliptic estimate and an explicit inverse are given and the hypoellipti city and the global solvability are obtained. Also, the structure of t he set of admissible points lambda is described exhaustively.