Acta mathematica scientia, Series B >
MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS
Received date: 2008-10-08
Revised date: 2011-02-05
Online published: 2012-03-20
Supported by
The research was supported by the National Natural Science Foundation of China (90818020, 60873206) and the Foundation of Innovation Team of Science and Technology of Zhejiang Province of China (2009R50024).
Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the so-called multivariate weighted Bernstein, Nikol’skiÏ, 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’skiÏ-type and Ul’yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.
CAO Fei-Long , LIN Shao-Bo . MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 471 -482 . DOI: 10.1016/S0252-9602(12)60030-7
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