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In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the weight functions have some singularities. In particular, we obtain new exact estimations for the growth of the modulus of orthogonal polynomials
We continue our investigation of the order of growth of the modulus of an arbitrary algebraic polynomial in the Bergman weight space, where the contour and weight functions have certain singularities. In particular, we deduce a Bernstein-Walsh-type pointwise estimate for algebraic polynomials in unbounded domains with piecewise asymptotically conformal curves with nonzero inner angles in the Bergman weight space.
We have obtained the pointwise Bernstein–Walsh type estimation for algebraic polynomials in the unbounded regions with piecewise asymptotically conformal boundary, having exterior and interior zero angles, in the weighted Lebesgue space.