Local Solvability for a Class of Nonhomogeneous Left Invariant Differential Operators on HR \bigotimes Rk (Journal of Partial Differential Equations, 1990)
In this paper we discuss tbe local solvability of the following nonhomogeneous left invariant differential operators on the nilpotent Lie group H_n⊗R^K: P(X, Y, T, Z) = Σ_{|α+β|+ζ+|y|≤m|α+β|+2l=a}a_{αβly}X^αY^βT^lZ^y where X_j, Y_j (j = 1, 2, …, n), T, Z_j(j = l, 2, …, K) are bases of left invariant vector fields on H_n⊗R^K and a_{αβly} are complex constants.
Keywords: Local solvability; nilpotent Lie group; nonhomogeneous left invariant differential operator