一类积分型算子在Orlicz空间内的逼近性质

Approximation Properties of Integral Type Operators in the Orlicz Spaces

以Baskakov算子和Beta算子为基础,构造了一类积分型算子,研究该算子在Orlicz空间内的逼近问题。利用Hardy-Littlewood极大函数、N函数的凸性、Jensen不等式以及K-泛函与连续模等工具,给出该算子在Orlicz空间内逼近的正、逆定理及等价定理。

In this paper,we discuss the approximation problem in Orlicz spaces of a kind of integral operators constructed on the basis of Baskakov operators and Beta operators.By using the Hardy-Littlewood maximal function,convex property of N function,Jensen Inequality,K-functional and modulus of smoothness,the integral operators approximation theorem and converse theorem are studied in Orlicz spaces and the approximation direct theorem,converse theorem and equivalent theorem of this operators are given in Orlicz spaces.