无界函数加权的点态逼近等价定理

A kind of weighted pointwise approximation direct and inverse theorem of unbounded continuous functions

利用二阶Steklov平均和Lorentz-Hermann引理 ,给出并证明了加权的点态逼近等价定理 ,该定理不仅用于对有界函数逼近 ,而且用于对无界函数逼近 ,并适用于一大类正线性算子 .

By means of second Steklov average and Lorentz-Hermann lemma, present and prove a kind of weighted equivalence theorem of pointwise approximation. The theorem is not only applicable to bounded continuous functions, but also to unbounded ones, and it is applicable to a large class of positive linear operators.