MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS  

作　　者：曹飞龙 林绍波 

机构地区：[1]Department of Information and Mathematics Sciences,China Jiliang University [2]Institute of Information and System Sciences,Xi'an Jiaotong University

出　　处：《Acta Mathematica Scientia》2012年第2期471-482,共12页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (90818020,60873206);the Foundation of Innovation Team of Science and Technology of Zhejiang Province of China (2009R50024)

摘　　要：Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.

关 键 词：Bernstein-type inequality Nikol＇skii-type inequality Ul＇yanov-type inequal-ity approximation 

分 类 号：O178[理学—数学]