Pointwise estimates of polynomials orthogonal on a circle with respect to a weight not belonging to the spaces $L^r$ ($r>1$).

Two-sided pointwise estimates are established for polynomials that are orthogonal on the circle $|z|=1$ with the weight $\varphi(\tau):=h(\tau)|\sin(\tau/2)|^{-1}g(|\sin(\tau/2)|)$ ($\tau\in\mathbb R$), where $g(t)$ is a concave modulus of continuity slowly changing at zero such that $t^{-1}g(t)\in L^1[0,1]$ and $h(\tau)$ is a positive function from the class $C_{2\pi}$ with a modulus of continuity satisfying the integral Dini condition. The obtained estimates are applied to find the order of the distance from the point $t=1$ to the greatest zero of a polynomial orthogonal on the segment [-1,1].