SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION: JUSTIFICATIONS

作     者：WangJianli ZhouSongping 

作者机构：ShaoxingArtsandScienceCollgeChina ZhejiangInstituteofScienceandTechnologyChina 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2003年第19卷第3期

页      面：280-288页

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Supported in part by National and Zhejiang Provincial Natural Science Foundations of China.Partof the work contained in this paper was done while the second named author was visiting Simon Fraser University Canada he thanks Dr.P.B.Borwein and the Depa 

主　　题：onesided approximation L p space modulus of continuity 

摘      要：The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.