摘要
The author gives some disagreement to the following result,which is published in [1].Let {L<sub>n</sub>(f(}be mass-concerntative,φ<sub>n</sub>→0+（n→∞）,0【α≤2 andC<sup>-1</sup>≤（φn+1）/（φn）≤C（n=1,2,…）for some constrant C】0.Then for any f∈C[-2a,2a],||L<sub>n</sub>（f）-f||σ[-a,a]=O（φ<sub>n</sub><sup>α</sup>）implies f∈Lip*α,whereLip*a={f∈C[-2a,2a]|w<sub>2</sub>（f,δ）[-2a,2a]=O（δ<sup>α</sup>）}.Then some similar results on C<sub>2π</sub>are given,and further some results on C[-2a,2a]areestablished by adding some proper conditions.
The author gives some disagreement to the following result, which is published in [1]. Let {L(n)(f(} be mass-concerntative, phi-n-->0 + (n --> infinity), 0 < alpha less-than-or-equal-to 2 and [GRAPHICS] for some constrant C > 0. Then for any f epsilon C[-2a, 2a], [GRAPHICS] implies f epsilon Lip*a, where [GRAPHICS] Then some similar results on C2-pi are given, and further some results on C[-2a, 2a] are established by adding some proper conditions.
