Orlicz空间内的Muntz有理逼近  

Muntz Rational Approximation in Orlicz Spaces

作　　者：张旭[1] 吴嘎日迪[1] ZHANG Xu;YVU Garidi(School of Mathematical Science,Inner Mongolia Normal University,Huhhot 010022,China)

机构地区：[1]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3期301-306,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)

摘　　要：有理逼近问题是函数逼近论的一个重要分支,为了在较大范围内研究有理逼近问题,本文在连续函数空间和L_p空间内研究有理逼近方法的基础上,利用修正的Bak算子,Hardy-Littlewood极大函数等工具,借助不等式技巧,研究了Muntz有理函数在Orlicz空间内的逼近问题,给出了光滑函数的Muntz有理逼近阶的两种估计,所得的结果明显优于前人的同类结果.Rational approximation of problem is an important branch of the function approximation theory, in order to study in a wide range of rational approximation, based on continuous function space and Lp space of rational approximation method, using modified Bak operators, Hardy-Littlewood maximal function, and inequality tech- nique, studied the Muntz rational function approximation problem in Orlicz spaces. In this paper, two kinds of estimates of the Muntz rational approximation order of smooth functions are given. The results obtained are obviously better than those of previous ones.

关 键 词：Bak算子 ORLICZ空间 Muntz有理逼近 

分 类 号：O174.41[理学—数学]