In 1993 motivated by some interesting questions in the theory of fully nonlinear equations, we proposed the study of the following problem. Consider a stratified, nilpotent Lie group G of step r, with Lie algebra g = V_1?…?V_r, and let X_1,…, X_m be a fixed orthonormal basis of the first layer V_1. Continue to denote with X_1, …, X_m the corresponding system of left-invariant vector fields on G.
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