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A maximum principle and some a priori estimates of a class of degenerate equations with X-ellipticity in the sense of distributions are established. A local comparison of the generalized Green function with its fundamental solutions is obtained. As an application, by means of the power of the Green function as a kernel function of a local integral, we also derive local Ḧolder continuity for nonlinear degenerate subelliptic equations. © 2012 American Mathematical Society.

Green functions for a class of nonlinear degenerate operators with X-ellipticity