On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szegö's condition

The author considers asymptotic properties of polynomials $\varphi_n(z)$, orthonormal on the unit circle $\Gamma$, with weights $f(z)$ that do not satisfy Szegö's condition. It is shown, in particular, that if $f(z)$ satisfies a Dini–Lipschitz condition, then $\lim_{n\to\infty}|\varphi_n(z)|=f(z)^{-1/2}$ uniformly on each set $\gamma\subset\Gamma$ on which $f$ has a positive lower bound.
Bibliography: 9 titles.