摘要
本文指出：文［４］中的广义单调序列不仅是拟单调序列概念的推广，而且也是Ｏ—正则拟单调序列概念的实质性推广．特别，序列的广义单调性不依赖于Ｏ－正则序列，本文还把文［３］的一个具有Ｏ－正则拟单调系数的Ｆｏｕｒｉｅｒ级数Ｌ１－收敛的充分必要条件推广到具有广义单调系数的Ｆｏｕｒｉｅｒ级数上，所得的结果推广了文［２］和［３］的主要结论．
In this paper we point out that the generalized monotonic sequence in [4] not only is an extension of quasimonotonicity but also a substantive extension of O-regularly varying quasimonotonicity. It is especially noteworthy that the generalized monotonicity of sequence is independent of O-regularly varying sequence. In this paper, the necessaryand sufficient condition for L1-convergence of Fourier series with O-regularly varying quasimonotonic coefficients in paper [2] is generalized to include Fourier series with generralized monotonic ceofficients, thereby expanding the main conclusions deduced in paper [2] and [3].
出处
《汕头大学学报（自然科学版）》
1996年第2期28-33,共6页
Journal of Shantou University：Natural Science Edition
关键词
广义
L^1-收敛
拟单调序列
傅里叶级数
单调序列
O-regularly varying sequence
quasimonotonicity
generalized monotonicity
Fourier series
L￣1-convergence
