Interference of the Weight and Boundary Contour for Algebraic Polynomials in Weighted Lebesgue Spaces. I

Abstract

We continue our investigation of the moduli of algebraic polynomials on the boundary contour with weight function in the case where the contour and the weight function have singularities with respect to their quasinorm in the weighted Lebesgue space. In particular, the exact estimates are obtained for polynomials orthonormal on the curve with respect to the weight function with zeros on the same curve.