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We consider linear second order nonvariational partial differential operatorsof the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where theX_{i}'s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfyingH\"ormander's condition and a_{ij} (i,j=1,2,...,q) are real valued, boundedmeasurable functions, such that the matrix {a_{ij}} is symmetric and uniformlypositive. We prove that if the coefficients a_{ij} are H\"older continuous withrespect to the distance induced by the vector fields, then local Schauderestimates on X_{i}X_{j}u, X_{0}u hold; if the coefficients belong to the spaceVMO 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 thepresence of the drift term X_{0}, so that our class of operators covers, forinstance, Kolmogorov-Fokker-Planck operators.

L^p and Schauder estimates for nonvariational operators structured on H\"ormander vector fields with drift