Lebesgue Sobolev orthogonality on the unit circle

This paper is devoted to the study of asymptotic properties of the orthogonal polynomials with respect to a Sobolev inner product 〈f(z),g(z)〉s = ∫02π f(eiθ))g(eiθ)dμ(θ)+∑k=1pλk∫02πfk(eiθ)g(eiθ)dθ2π, z=eiθ, with dμ(θ) a finite positive Borel measure on [0, 2π] with an infinite set as support verifying the Szegő condition, λ1 > 0, λk ⩾ 0 (k = 2,…, p) and dθ2π the normalized Lebesgue measure on [0, 2π]. m is to extend some previous results that we have obtained in [2, 3] when the measure μ belongs to the Bernstein-Szegő class and p = 1.