On the properties of the orthogonal polynomials with weight along the piecewise smooth contour

In this work, we investigate the order of the height of the modulus of orthogonal polynomials over a piecewise smooth contour and also arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and weight function have some singularities. We analyze the different conditions with respect to the degree of singularity of weight and contour.