加权Orlicz空间中的最佳多项式逼近

Best Polynomial Approximation in Weighted Orlicz Space

在加Jacobi权的Orlicz空间中研究了最佳多项式逼近问题,利用De la ValléePoussin平均,凸函数的Jensen不等式,Holder不等式以及相关分析技巧给出了次数不超过n的多项式在Orlicz空间内加Jacobi权的Jackson-Favard型估计。

In this paper,the optimal polynomial approximation problem is studied in Jacobiweighted Orlicz spaces,and the Jackson-Favard type estimation of the polynomial whose degree at most n are given by using the De la Vallee Poussin means,the Jensen inequality of the convex function,the inequality and the related analysis techniques.