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=-mΣi,j=1X*j(aij(x)Xiu)+vu=μis studied, where X = {X1,…, Xm} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and μ a nonnegative Radon measure. The HSlder continuity of the solution is proved when μ satisfies suitable growth condition, and a converse result on the estimate of # is obtained when u is in certain HSlder class.