Bernstein – Walsh-type polynomial inequalities in domains bounded by piecewise asymptotically conformal curve with nonzero inner angles in the Bergman space

Abstract

UDC 517.5
We continue the 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 a piecewise asymptotically conformal curve with nonzero inner angles in the Bergman weight space.