Resumen de Inequalities for products of polynomials II

Igor E. Pritsker, Stephan Ruscheweyh

• In this paper, we continue the study of inequalities connecting the product of uniform norms of polynomials with the norm of their product, begun in [28]. Asymptotically sharp constants are known for such inequalities over arbitrary compact sets in the complex plane. We show here that such constants can be improved under some natural additional assumptions. Thus we find the best constants for rotationally symmetric sets. In addition, we characterize all sets that allow an improvement in the constant when the number of factors is fixed, and find the improved value.