Ba空间中Beta算子的逼近等价定理

Approximation Equivalent Theorem of the Beta Operator in Ba Spaces

引入Ba空间中K-泛函与光滑模的定义,借助K-泛函与光滑模的等价性,研究了Beta算子在Ba空间中逼近的等价问题,得到了逼近等价定理,所得的结果包含了Lp空间中的相应结果.

In this paper,the definitions of K-functional and modulus of smoothness are introduced,and the equivalent theorem of Beta operator in Ba spaces is established by using the equivalence of K-functional and modulus of smoothness.The result in this paper involves the corresponding result in Lp spaces.