On the lifting and approximation theorem for nonsmooth vector fields Marco BramantiLuca BrandoliniMarco Pedroni 53C17nonsmooth Hoermander's vector fieldsliftingsubelliptic distance We prove a version of Rothschild-Stein's theorem of lifting and approximation and some related results in the context of nonsmooth Hoermander's vector fields for which the highest order commutators are only Hoelder continuous. The theory explicitly covers the case of one vector field having weight two while the others have weight one. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4298 10.1512/iumj.2010.59.4298 en Indiana Univ. Math. J. 59 (2010) 2093 - 2138 state-of-the-art mathematics http://iumj.org/access/