Regularity and the Cesàro–Nevai class

We consider OPRL and OPUC with measures regular in the sense of Ullman–Stahl–Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [−2,2] implies lim_(N→∞)N^(-1)[∑_(n=1)^N(a_n-1)^2 + b_n^2] = 0