摘要
本文把熟知的函数空间ABV的一些性质,推广到更大的函数空间上去,并给出了φBV中函数的富里埃系数的阶的估计,同时给出了φBV中函数的富里埃级数绝对收敛的一个充分条件.
AbstractIn this paper, some properties on the class of function ΦBV were discussed. If f∈ΦBV, then its nth fourier cofficient f(n)=O(gn-3 (VΦ(f.I))); if f∈ΦBV then f(n)=o (gn-1 (VΦ (f,I))), where g is a convex function. Its integral modulus of continutity W(f ,δ)L1=O(gn-1(VΦ(f,I))). In the last part of the paper we gave a sufficient condition for absolute convergence of σ[f], where σ[f]is Fourier Series of f(f∈ΦBV).
出处
《杭州大学学报（自然科学版）》
CSCD
1996年第3期205-211,共7页
Journal of Hangzhou University Natural Science Edition
关键词
Φ-序列
Φ有界变差函数
积分连续模
函数空间
: Φ-sequence
function of c-bounded variation
integral modulus ofcontinuity
