In this article, we prove the continuity of the horizontal gradient near a C-1,C-Dini non-characteristic portion of the boundary for solutions to Gamma(0,Dini) perturbations of horizontal Laplaceans as in (1.1) below, where the scalar term is in scaling critical Lorentz space L(Q, 1) with Q being the homogeneous dimension of the group. This result can be thought of both as a sharpening of the Gamma(1,alpha) boundary regularity result in 4 as well as a subelliptic analogue of the main result in 1 restricted to linear equations.
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