Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 95-108.

• Articles • Previous Articles     Next Articles

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. 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.

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

CLC Number: 

  • 41A17
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