On Szeg?'s Inequality

Abstract:

      Let p_n(x) be the space of algebraic polynomials with degree at most n. This paper obatins ‖p′_n(x)e^-x‖_[0,∞)≤(6.3n+1)‖p_n(x)e^-x‖_[0,∞);If moreover p_n(x) is even or odd function, then ‖p′_n(x)e^-x‖_[0,∞)≤(1.8+7n^1/2)‖p_n(x)e^-x‖_[0,∞).