Regularity and the Cesà ro-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 limN→∞N−1[∑n=1N(an−1)2+bn2]=0.