On Turán type inequality with doubling weights and A * weights

Abstract

LetH n be the set of real algebraic polynomials of degreen, whose zeros all lie in the interval [−1,1]. The well known Turan type inequalities tell us that forf(x)∈H n , it holds ‖f′‖≥C√n‖f‖. This note deals with the weighted Turan type inequalities with the weights having inner singularities underL p norm for 0<p≤∞. 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.