Orlicz 空间中加权光滑模与K -泛函的等价性及其应用

数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 95-108.

Orlicz 空间中加权光滑模与K -泛函的等价性及其应用

韩领兄, 吴嘎日迪, 刘国锋

1.内蒙古民族大学数学科学学院内蒙古通辽 028000;
2.内蒙古师范大学数学科学学院呼和浩特 010022

收稿日期:2012-09-21 修回日期:2013-10-12 出版日期:2014-02-25 发布日期:2014-02-25
基金资助:
国家自然科学基金(11161033)、内蒙古自然科学基金(2010MS0119)和内蒙古师范大学人才工程基金(RCPY-2-2012-K-036)资助.

The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and it's Application

HAN Ling-Xiong, Wu Garidi, LIU Guo-Feng

1.College of Mathematics Science, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao 028000;
2.College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022

Received:2012-09-21 Revised:2013-10-12 Online:2014-02-25 Published:2014-02-25
Supported by:
国家自然科学基金(11161033)、内蒙古自然科学基金(2010MS0119)和内蒙古师范大学人才工程基金(RCPY-2-2012-K-036)资助.

摘要/Abstract

摘要：

首先介绍了由Young 函数生成的Orlicz空间L*_Φ[0, ∞), 然后利用归纳假设和分解方法证明了r阶加权光滑模与加权K -泛函的等价性, 最后作为光滑模的应用给出了Gamma算子在L*_Φ[0, ∞) 空间内加权同时逼近的B -型强逆不等式.

关键词: Orlicz 空间, Young 函数, K -泛函, 加权光滑模

Abstract:

First, the Orlicz space L*_Φ[0, ∞) corresponding to the Young function Φ(x) is introduced. Then by the inductive assumption and the decomposition method, the equivalence theorem between K-functional and r-th modulus of smoothness in Orlicz space L*_Φ[0, ∞) is given. Finally, as an application of the modulus, a strong converse inequality of B type for the Gamma operators is obtained.

Key words: Orlicz Space, Young function, K-functional, Smooth modulus with weights

中图分类号:

41A17

韩领兄, 吴嘎日迪, 刘国锋. Orlicz 空间中加权光滑模与K -泛函的等价性及其应用[J]. 数学物理学报, 2014, 34(1): 95-108.

HAN Ling-Xiong, Wu Garidi, LIU Guo-Feng. The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and it's Application[J]. Acta mathematica scientia,Series A, 2014, 34(1): 95-108.

[1]	乔丹, 杨美金, 陈建仁. 极大高阶交换子的端点估计[J]. 数学物理学报, 2012, 32(2): 320-335.
[2]	郭顺生, 刘国芬, 宋占杰. 关于Bernstein-Durrmeyer-Bézier算子在L_p}空间中的逼近[J]. 数学物理学报, 2010, 30(6): 1424-1434.