Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients

The purpose of this paper is to investigate the local regularity of the nondivergence degenerate elliptic operator with lower order terms in generalized Morrey spaces, structured on a family of Hormander's vector fields without an underlying group structure. The coefficients of the second order terms of the operator are real valued, bounded and measurable functions, such that the uniform ellipticity condition holds; moreover, they belong to the space VMO (Vanishing Mean Oscillation), with respect to the subelliptic metric induced by the vector fields. The coefficients of the lower order terms of the operator are in suitable generalized Morrey spaces.