On Turan type inequality with doubling weights and A weights

摘要

Let H_n be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turan type inequalities tell us that for the point f(x) Delong to the set H_n it holds ||f'|| > = C n~(1/2)||f||. This note deals with the weighted Turan type inequalities with the weights having inner singularities under L~p norm for 0< = fnfinity. Our results essentially extend the result of Wang and Zhou (2002), and the method used in this paper is simpler and more direct than that of Wang and Zhou (2002). The results and methods have their own values in approximation theory and computation.