FUNCTIONS OF BOUNDED MEAN OSCILLATION AND RELATED TOPICS

有界平均振荡的函数及相关主题

• 批准号: 60540084
• 负责人: WATARI Chinami
• 金额: $ 0.77万
• 依托单位: YAMAGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60540084/
• 关键词: FUNCTIONS OF BOUNDED MEAN OSCILLATION; BMO; BERNSTEIN INEQUALITY; POLYNOMIAL APPROXIMATION; 指数型作用素

It is very well known that the functions of bounded mean oscillation are characterized by means of Poisson integral. In these investigations, we have succeeded in finding out that the same characterization is possible through a rather wide class of singular integrals : in particular, we can characterize the functions of bounded mean oscillation by means of Cesaro means of their Fourier series. Also, analogue of Bernstein inequality for the space BMO is obtained. See appended pamphlet, part 1.As to the approximation theory, results on exponential type operators are obtained. They are also included together with a preliminary version of Lecture notes on Approximation Theory of periodic functions. In our intension, some other topics such as approximation by positive linear operapors, operating functions on some subclasses of A, would be included ; we hope, in a near future, to publish a completed version.

众所周知，有界平均振荡函数是用泊松积分来刻画的。在这些研究中，我们成功地发现，通过一类相当广泛的奇异积分，同样的刻画是可能的：特别地，我们可以利用有界平均振荡函数的傅立叶级数的Cesaro平均来刻画它们。还得到了BMO空间的Bernstein不等式的类比。关于逼近理论，得到了关于指数型算子的结果。它们也包括在初版的关于周期函数逼近理论的讲稿中。在我们的内容中，还将包括其他一些主题，如正线性算子的逼近，A的某些子类上的运算函数，我们希望在不久的将来出版一个完整的版本。

项目成果

佐藤邦夫: 実解析セミナー. 182-186 (1986)

佐藤邦男：实分析研讨会182-186（1986）

WATARI, Chinami: "Remark on Lebesgue points and Singnlar Integrals" Seminar on Real Analysis. 33-34 (1985)

WATARI, Chinami：“关于勒贝格点和奇异积分的评论”实分析研讨会。

渡利千波: 実解析セミナー. 33-34 (1985)

Chinami Watari：实践分析研讨会 33-34 (1985)。

SATO, Kunio: "On Uniform Approximation" Seminar on Real Analysis. 182-186 (1986)

SATO, Kunio：“关于均匀近似”实分析研讨会。

WATARI,C.: "Lectures on Approximation Theory" 25

WATARI,C.：“近似理论讲座”25