  We consider linear second order nonvariational partial differential operators
of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the
X_{i}'s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying
H\"ormander's condition and a_{ij} (i,j=1,2,...,q) are real valued, bounded
measurable functions, such that the matrix {a_{ij}} is symmetric and uniformly
positive. We prove that if the coefficients a_{ij} are H\"older continuous with
respect to the distance induced by the vector fields, then local Schauder
estimates on X_{i}X_{j}u, X_{0}u hold; if the coefficients belong to the space
VMO with respect to the distance induced by the vector fields, then local L^{p}
estimates on X_{i}_{j}u, X_{0}u hold. The main novelty of the result is the
presence of the drift term X_{0}, so that our class of operators covers, for
instance, Kolmogorov-Fokker-Planck operators.
