Turan type converse Markov inequalities in L-q on a generalized Erod class of convex domains

摘要

P.Turan was the first to derive lower estimations on the uniform norm of the derivatives of polynomials p of uniform norm 1 on the disk D := {z is an element of C : vertical bar z vertical bar <= 1} and the interval I := [-1, 1], under the normalization condition that the zeros of the polynomial p in question all lie in D or I, resp. Namely, in 1939 he proved that with n := deg p tending to infinity, the precise growth order of the minimal possible derivative norm is n for D and root n for II.