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This paper is concerned with the regularity of weak solutions to the general nonlinear sub-elliptic systems related to Hörmander's vector fields. Based on the reverse Hölder inequality established by Gianazza, the L p estimates for weak solutions to the systems under the super-quadratic controllable growth condition and the natural growth condition are established, respectively. Then we obtain the Hölder continuity for weak solutions.doi:10.2206/kyushujm.63.301 fatcat:dgqh3rsuarfx5hefn7ee66fspu