Extension inside the disk of asymptotics for Sobolev orthogonal polynomials

In this paper, we consider a general Sobolev inner product on the unit circle of the follwing type: , with μj (j = 0, …, p) finite positive Borel measures on [0, 2π] and p a positive integer p 1. Under the assumption that the Caratheodory functions of measures μ0,…,μp−1 and the Szeg function of measure μp have analytic extension outside the open unit disk, we prove that Szeg ʹs asymptotic formula holds true for the Sobolev orthogonal polynomials.