Sobolev-Morrey spaces related to an ultraparabolic equation

Let us consider the class of hypoelliptic operators Lu = Sigma(i,j=1)(m0)a(i,j)(z)delta(xi,xj)u + Sigma(i,j=1)(N)b(i,j)x(i)delta(xj)u - delta(t)u where z = (x, t) is an element of RN+1, 0 < m(0) less than or equal to N the coefficients a(i,j) belong to the space of vanishing mean oscillation functions (VMOL) and B = (b(i,j)) is a constant real matrix. In this paper we prove that a strong solution to the differential equation Lu - f, with the known term f in the Morrey space L-p,L-lambda, belongs to a suitable Sobolev-Morrey space S-p,S-lambda. Then we prove some Mor-ey-type imbedding results that give a local Holder continuity of the solution u.