Approximation on set of total measure of Bochner-Riesz means below the critical index

In this paper it has been considered convergence and approximation for functions inSobolev Spaces L_m~1(R~n)by Bochner-Riesz means below the critical index.A theorem that ofprecise approximation orders on set of total measure has been proved.     

多重共轭Fourier级数的Bochner-Riesz平均的一致逼近

本文研究了多重共轭 Fourier级数的 Bochner-Riesz平均对索伯列夫空间W~(2,∞)中函数的一致逼近问题。得到了如下结论:当共轭核中的齐次调和多项式为二次时,其逼近阶可达1/R~2。而对于非二次的齐次调和核,其逼近阶为log R/R~2,且以上二个逼近阶都是最优的。