Abstract: | Let B be a domain in the complex plane, let pn(z) and Pn(z) be polynomials of degree n where the zeros of Pn(z) lie in, let(z) be a finite function,(z) 0, z. We consider the problem of estimating from above the functions L[pn(z)]=(z)pn(z) – wpn(z), z, if ¦pn(z)¦ ¦Pn(z)¦ for zB. Under some very general conditions on B, z, (z), and w we prove the inequality ¦L[pn(z)]¦ ¦L[Pn(z)]¦.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 431–440, April, 1968. |