| Orlicz空间中加权光滑模与K-泛函的等价性及其应用 |
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| 引用本文： | 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(A辑),2014,34(1):95-108. |
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| 作者姓名： | 韩领兄 吴嘎日迪 刘国锋 |
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| 作者单位： | 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 |
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| 基金项目： | 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. |
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| 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.
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| 关 键 词： | Orlicz空间 Young函数 K-泛函 加权光滑模. |
| 收稿时间： | 2012-09-21 |
| 修稿时间： | 2013-10-12 |
The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and it's Application |
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| 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,2014,34(1):95-108. |
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| Authors: | HAN Ling-Xiong Wu Garidi LIU Guo-Feng |
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| Institution: | 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 |
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| Abstract: | First, the Orlicz space L*Φ0, ∞) 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*Φ0, ∞) is given. Finally, as an application of the modulus, a strong converse inequality of B type for the Gamma operators is obtained. |
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| Keywords: | Orlicz Spacezz Young functionzz K-functionalzz Smooth modulus with weightszz |
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