摘要
对f∈L′(T),设S_n(f)=S_n(f,t)为f的Fourier级数的n项部分和,又设{R(n)}为O^-正则变化序列。本文的主要结果是:对1<P≤2,若存在一个正整数n_θ。当n>n_0时有K_n^(?)(f)=1gR(n),则有 i) {Sn(f,t)}(t≠0)在T中几乎处处收敛于f ii) {Sn(f)}依L^1(T)^-范数收敛于f的充分必要条件是(?)(n)1g|n|=0(1),|n|→∞。本文结出的关于{R(n)}的条件比stanojevic在参考文献[1]中结出的条件弱,因此是stanojevic 1987年在参考文献[1]中所获结果的推广。
For f∈L'(T), Let Sn(f) be n-th partial Sum of the Fourier series of f Let {R(n)} be an O-regularly varying sequence. The main theorem of this paper is the following: Let 1<p≤2, if K_(?)~p(f)=lgR(n) for n>n_0 then ⅰ) for t≠0, {sn(f. t)} convergence to f a、e、in T, and ⅱ) {sn(f)} convergence to f in L'(T)-norm if and-only if(?) (n) lg|n|=o(1) as |n|→∞. Onr condition On {R(n)} is weaker than that of stanojevio. This is an extention from the conclusion obtained by stanojevic is references is 1987
出处
《东北师大学报（自然科学版）》
CAS
CSCD
1989年第4期13-20,共8页
Journal of Northeast Normal University(Natural Science Edition)
关键词
正则变化联列
收敛模
L^
(T)^-范数
Convergonce Moduli, convergence in L' (T)-norm, Regularly varying sequence
