Holder continuity for a class of X-elliptic equations with singular lower order term

The regularity for a class of X-elliptic equations with lower order term Lu + vu = - Sigma(m)(i,j=1)X(j)(*)(a(ij)(x)X(i)u) + vu = mu is studied, where X = {X(1), ..., X(m)} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and mu a nonnegative Radon measure. The Holder continuity of the solution is proved when mu satisfies suitable growth condition, and a converse result on the estimate of mu is obtained when u is in certain Holder class.