修正的积分型求和算子在Orlicz空间中的逼近（英文）  

Approximation by Modified Summation Integral Type Operators in Orlicz Spaces

作　　者：韩领兄[1] 吴嘎日迪[2] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028000 [2]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《应用数学》2017年第3期613-622,共10页Mathematica Applicata

基　　金：Supported by the Foundation of National Natural Science of China(11161033,11461052);the Foundation of National Natural Science of Inner Mongolia(2014BS0106,2016MS0118);the Scientific Research Project of Inner Mongolia University for Nationalities(NMDYB15087)

摘　　要：本文介绍由Φ(x)构成的Orlicz空间L_Φ~*[0,∞),并介绍Orlicz空间的Hardy-Littlewood性质.然后给出Orlicz空间中修正的加权K-泛函与加权连续模的等价定理,最后建立修正的积分型求和算子在Orlicz空间中逼近的正、逆定理和等价定理.从而推广了该算在L_p[0,∞)空间中逼近性质.In the present paper, the Orlicz spaces LΦ^＊[0, ∞）, which corresponds to the Young function Φ（x）, are introduced and the Hardy-Little-wood property of the Orlicz spaces is given. Then the equivalence theorem between the modified weighted K-functional and the weighted modulus of smoothness is established in Orlicz space. Finally, the direct, inverse and equivalent theorems of modified summation integral type operators are established in Orlicz space then generalized the approximation property of this type operators in LP [0, ∞） space.

关 键 词：ORLICZ空间 YOUNG函数 K-泛函 光滑模 

分 类 号：O174.41[理学—数学]