Fourier-Laplace级数的点态强逼近

POINTWISE ESTIMATE OF STRONG APPROXIMATION WITH RESPECT TO FOURIER-LAPLACE SERIES

设λ=n-2/2,1<p≤2及α∈(λ-1+1/p,λ].用连续模给出了Lp(Σn-1)中函数用其Fourier-Laplace级数的α阶Cesàro平均等收敛算子强逼近的点态收敛速度.

The convergence rate of pointwise strong approximation by the equiconvergent operators of Cesàro means at the indices α∈（λ-1＋1/p,λ] for functions in L^p（∑n-1） （1〈 p ≤ 2） is given in terms of localmodulus of continuity, where λ=n-2/2 is the critical index.