Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift

Suppose that X0,X1,…,Xm are left invariant real vector fields on the homogeneous group G with X0 being homogeneous of degree two and X1,…,Xm homogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kind L=∑i,j=1maijXiXj+a0X0, where a0≠0 and (aij) is a constant matrix satisfying the elliptic condition on Rm. By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates for L