$L_{p}$ inequalities for the growth of polynomials with restricted zeros

Abstract

. Let P ( z ) = P n ν =0 a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1, then for 1 ≤ p < ∞ and R > 1, Boas and Rahman proved In this paper, we improve the above inequality for 0 ≤ p < ∞ by involving some of the coefficients of the polynomial P ( z ). Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.