Gamma算子加权逼近的点态结果

The Pointwise Result on Weighted Approximation for the Gamma Operators

利用光滑模ω2φλ(f,t)w讨论了Camma算子的加权点态逼近,得到如下的逼近等价定理:设wf∈CB(R+),0<α<2,0≤λ≤1,则w(x)｜Gn(f,x)-f(x)｜=Oφ1-λ(x)nα ω2φλ(f,t)w=O(tα).这个结果扩展了以前关于这方面的一些结果.

Make use of ω~2_(φ~λ)(f,t)_w to give the pointwise equivalent result on Gamma operators:If wf∈C_B(R_+),0<α<2,0≤λ≤1,then w(x)｜G_n(f,x)-f(x)｜=Oφ^(1-λ)(x)n~αω~~2_(φ~λ)(f,t)_w=O(t~α). This result is generalization of some previous ones.