三角级数属于Ba空间的充分必要条件

数学物理学报 ›› 2008, Vol. 28 ›› Issue (6): 1038-1045.

三角级数属于Ba空间的充分必要条件

虞旦盛¹|周颂平²

(1.杭州师范大学数学系杭州 310018|2.浙江理工大学数学研究所杭州 310018)

收稿日期:2006-01-08 修回日期:2007-11-10 出版日期:2008-12-25 发布日期:2008-12-25
通讯作者: 虞旦盛
基金资助:
西南石油学院国家重点实验实开放项目(PLN0613)资助

The Sufficient and Necessary Conditions for Trigonometric Series Belonging to Ba Spaces

Yu Dansheng¹|Zhou Songping²

(1.Department of Mathematics, Hangzhou Normal University,Hangzhou 310018|2.Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018)

Received:2006-01-08 Revised:2007-11-10 Online:2008-12-25 Published:2008-12-25
Contact: Yu Dansheng

摘要/Abstract

摘要：

该文给出了正弦级数和余弦级数在系数满足NBV条件时属于Ba空间的充分必要条件,所得结论
为Ba空间中的首个此类结果,同时也是对L_p空间中已有结论的本质性推广.

关键词: 三角级数, NBV条件, Ba空间, 充分必要条件

Abstract:

The present paper gives a sufficient and necessary condition for sine series and cosine series, with their coefficients satisfying NBV condition, belonging to Ba spaces. This is the first result on Ba spaces and can be regarded as an essential generalization of that on L_p spaces.

Key words: Trigonometric series, Monotonicity, Ba spaces, Suffcient and necessary condition

中图分类号:

42A20

虞旦盛|周颂平. 三角级数属于Ba空间的充分必要条件[J]. 数学物理学报, 2008, 28(6): 1038-1045.

Yu Dansheng|Zhou Songping. The Sufficient and Necessary Conditions for Trigonometric Series Belonging to Ba Spaces[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1038-1045.

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