Lupas-Baskakov型算子在Orlicz空间内逼近的强逆不等式

Approximation of Lupas-Baskakov Operators Strong Converse Inequality in Orlicz Space

本文利用Hardy-Littlewood极大函数、光滑模和K-泛函之间的等价关系、N函数的凸性、算子矩量估计及Jensen不等式等工具,研究了由陈文忠定义的LupasBaskakov型算子在Orlicz空间内的逼近性质,给出并证明了该算子在Orlicz空间内逼近的强型逆定理.由于Orlicz空间比连续函数空间和L_p空间涵盖更广泛,其拓扑结构也比L_p空间复杂得多,所以本文的结果具有一定的拓展意义.

In this paper, the Lupas-Baskakov function defined by Chen Wenzhong is studied by means of the Hardy-Littlewood great function, the equivalence relation between the smooth function and the functional, the convexity of the function, the operator moment estimation and the Jensen inequality. Baskakov type operators in Orlicz spaces, the strong converse theorem of the operators in Orlicz spaces is given and proved. Because Orlicz space is more extensive than space function and L_p-spaces function, the topological structure of Orlicz space is much more complex than that of space, so the result of this paper has a certain extend meaning.