加权Bernstein-Durrmeyer算子在Orlicz空间中的加权逼近

Weighted Approximation of Weighted Bernstein-Durrmeyer Operators in Orlicz Spaces

本文借助凸函数的Jensen不等式、Orlicz空间中的H?lder不等式、光滑模和Hardy-Littlewood极大函数等工具,研究了加权Bernstein-Durrmeyer算子在加权Orlicz空间内的逼近问题,并建立了相应的逼近正定理和等价定理。

This paper mainly discussed the weighted approximation problem of the weighted Bernstein-Durrmeyer operators in the Orlicz spaces.By using the Jensen inequality,the H?lder inequality,K-functional,the Hardy-Littlewood maximum function and related analysis techniques,the paper established corresponding approximation direct theorem and equivalence theorem.