L^1空间正系数多项式的倒数逼近

On the Approximation by Reciprocals of Polynomials with Positive Coefficientes in L^1 Spaces

本文讨论了L1空间函数的正系数多项式的倒数逼近的Jackson型估计问题,并证明了:如果f(x)∈L[0,1]1,f(x)≥0,f(x)(?)0,则存在一个次数不超过n正系数多项式qn(x)∈Πn(+),使得||f-1/qn||L1≤Cω(f,n-1/2)L1,其中Πn(+)表示所有次数不超过n的正系数多项式的全体.

The present paper investigates approximation by reciprocals of polynomials with positive coefficients in L[0,1]1, space and proves that if f(x)∈L[0,1]1, f(x)≥0, f(x)(?)0, then there exists a qn(x)∈Πn(+) such that ||f-1/qn||L1≤Cω(f,n-1/2)L1, where Πn(+) indicates all polynomials of degree n with positive coefficients.