关于正系数多项式导数的点态不等式

The Pointwise Inequality for Derivatives of Polynomials with Positive Coefficients

本文讨论正系数多项式导数的点态不等式,建立相应的结果。

This note discusses the pointwise inequality for derivatives of polynomials with positive coefficients. We establish the following theorem. Theorem. If f(x)∈Ⅱ+n, then where Ⅱn+ is the class of algebraic polynomials of degree n with positive coefficients, ||f||Lp[-1,1] is the Lp-norm of f on [-1,1], and Cr is a constant depending upon r only.