Orlicz空间中复系数多项式倒数逼近  

Approximation by Reciprocal of Polynomials with Complex Coefficients in Orlicz Space

作　　者：吴晓红 吴嘎日迪[3] 黄俊杰[1] WU Xiaohong;WU Garidi;HUANG Junjie(College of Mathematics Science, Inner Mongolia University, Hohhot 010021, China;Department of Mathematics, Hohhot Minzu College, Hohhot 010051, China;College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院数学系,呼和浩特010051 [3]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《应用泛函分析学报》2018年第2期136-141,共6页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11761055);内蒙古自治区自然科学基金(2017MS0123);自治区高等学校科学研究项目(NJZY17234)

摘　　要：本文利用K-泛函、加权连续模与极大函数等工具,借助不等式技巧,在Orlicz空间内研究了复系数多项式的倒数逼近问题,得到了收敛速度估计的结果.By the study of Leviatan and Lubinsky, we found that when we study the approximation by reciprocal of polynomials with real coefficients in norm, we always assume that the sign of f（x） dose not change on the interval. If we want to get rid of this restriction we need to talk about the reciprocal polynomial approximation with complex coefficients. And we also know that, in the Lp space whether the function f（x）changes sign or not we able to get a approximation expression. At last in order to obtain some conclusions in a wider space Orlicz space, we studied the approximation problems of reciprocal of polynomials with complex coefficients in Orlicz spaces by using the Kfunctional, weighted modulus of continuous and extreme maximum function tools etc,with the help of techniques of inequality, we obtain the estimation of convergence rate.

关 键 词：ORLICZ空间 加权连续模 逼近 多项式 

分 类 号：O174.41[理学—数学]