Post-Widder算子加权的同时逼近等价定理

Weighted LP-approximation of Derivatives by the Method of Post-Widder Operators

本方借助加权D－T光滑模，给出了Post-Widder算子加权的同时逼近的特征刻划定理．

We consider Post-Widder operators Pn(f; x) on suitable Sobolev type subspace of Lp[0, +∞)(1≤p ＜＋∞)or C[0,＋∞)n∩ L∞[0,＋∞)(p=＋∞) and characterize the global rate of ap-proximation of derivatives f(r) through corresponding derivatives (Pnf)(r) in an approxpriate weighted Lp-metric (1≤p≤＋∞) by the rate of Ditzian and Totik’s r-th order weighted moduli of smeethness.