摘要
本文在[2]及[3]的基础上给出了多重Fourier级数及其共轭级数的Bochner—Riesz平均的Fejér和σ_R~α及(?)_R~α(f)对于α>(n-3)/2的定点收敛性定理。同时对于连读函数f,给出了σ_R~α(f)(α>(n-3)/2)的余项为二阶连续模形式的精确表达式。最后证明了对于L2中的函数f,σ_R^0及(?)_R^0(f)几乎处处收敛于f及其共轭函数f~*。
In this paper based on[2] and (3) the result about pointwise convergence of Fejer sum of Bochner-Riesz means of the Fourier series and its conjugateseries ( denoted [by σRa(f) and σRa(f) respectively ) has been obtained. For continuous function f, it has been given the precise expression for σRa(f) ( a>(n-3)/2) with modulus of continuity of order 2 for the residual term. Atlast we have proven that σR0(f) and σR0(f) converge almost everywhere to fand its conjugate function f* respectively for f in L2.
