Convergence Problems and Integral Inequalities

收敛问题和积分不等式

• 批准号: 07640241
• 负责人: WATARI Chinami
• 金额: $ 1.47万
• 依托单位: Tohoku Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640241/
• 关键词: Bernstein inequality; BMO; Absolute convergence; DIGITAL SUM; 拡散移流型方程式; Bernstein 不等式; multinomal measure; digital sums; 拡散・移流型方程式; multinomial muasure; Bernstein型不等式; 積分不等式; 高木関数

The purpose of the project was twofold : first, to determine the convergence behavior of the Fourier or Walsh Fourier series of so-called Zygmund class and second, to obtain integral inequalities which can be used in various scenes of mathmatical analysis.The first problem turns out to be very difficult to attack, so our main effort centered around the second problem, intertwining with other branches of mathematical analysis, especially the theory of approximation of functions. Since very few results are reported on the approximation of functions belonging to the space BMO, the chief investigator tried to make up lecture notes on the topic, which will be appended in this report.The Bernstein inequality is proved in this setting, then it is improved so as to yield easy treatment for applications. As a result, the whole theory is based on a few simple "tools", and this will show the extent of the vast extent of Bernstein's ideas.

该项目有两个目的：第一个问题是确定所谓Zygmund类的Fourier或沃尔什Fourier级数的收敛性，第二个问题是得到可用于各种数学分析场合的积分不等式，第一个问题是很难解决的，所以我们的主要工作围绕第二个问题展开，与数学分析的其他分支交织在一起，尤其是函数逼近理论。由于很少有结果的报告属于空间BMO的函数的逼近，首席研究员试图弥补讲座笔记的主题，这将被附在这份报告中，证明了伯恩斯坦不等式在这种设置，然后它是改进的，以便产生易于处理的应用。因此，整个理论是建立在几个简单的“工具”上的，而这将显示出伯恩斯坦思想的广阔范围。

项目成果

Chinami WATARI: "An Example of Trial-and-Error in Mathematics : How an Integral Inequality Was Established" Journal of Human Informatics. 1. 85-92 (1996)

Chinami WATARI：“数学试错的一个例子：积分不等式是如何建立的”人类信息学杂志。

渡利千波: "数字における試行錯誤の例-1つに積分不等式が出来るまで-" 人間情報学研究. 創刊中. 85-92 (1996)

Chinami Watari：“数字试错的例子 - 直到创建一个积分不等式 -”人类信息学研究 85-92 (1996)。

NAKAGAWA,Kiyokazu: "Asymptotic Behavior of Solutions of Impulsive Semilinear Parabolic Equations" Nonlinear Analysis,Theory,Methods and Applications. 30. 2725-2734 (1997)

NAKAGAWA，Kiyokazu：“脉冲半线性抛物型方程解的渐近行为”非线性分析、理论、方法和应用。

Kiyokazu NAKAGAWA: "Asymptotic Behavior of Solutions of Impulsive Semilinear Parabolic Equations" Nonlinear Analysis, Theory, Methods and Applications. 30. 2725-2734 (1997)

Kiyokazu NAKAGAWA：“脉冲半线性抛物型方程解的渐近行为”非线性分析、理论、方法和应用。

渡利千波: "数学における試行錯誤の例-1つの積分不等式が出来るまで" 人間情報学研究. 創刊号. 85-92 (1996)

Chinami Watari：“数学中的试错示例 - 直到创建一个积分不等式”人类信息学研究第一期（1996）。