Harmonic Analysis and its Applications

谐波分析及其应用

基本信息

批准号：
08454022
负责人：
IGARI Satoru
金额：
$ 4.86万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

The problem of the harmonic analysis is often reduced to the invitational of translation invariant operators. As a useful real analysis method of such operators, there is the singular integral theory. However, we pay attention to the important translation invariant operators which aren't satisfied with the category of that theory. There, the Kakeya maximal function plays an important role an auxiliary function. Igari defines a maximal function which has a special base, and gave an estimate which gives the best possible estimate for radial functions, and also a partially Bourgain's result.Arai studied, form the viewpoint of the harmony analysis, the elliptic partial differential operators which degenerate in all points in the boundary, such as operators in pseudo-convex domain of the Stein manifolds and in the manifolds with theta-structure. He gets a basic result in the harmony analysis of such operators and is preparing a paper on it. Also, he found he fact which has a possibility to solve the pointwise Fatou problem for functions of several complex variables.It is studied for a long time the uniqueness of the solution of the Navier-Strokes equation, but it is still an unsolved major theme. Masuda introduced a quite new way which is of real variable method for this problem, and found a beginning of solving the problem. This result was reported in the international conference held in Verona. Also, he solved the conjecture on the classification of the minimal surfaces of constant curvature in two dimensional complex space from by the collaboration with K.Kenmotsu..Saito developed an important tool for the study of the monotone complete C*-algebra by giving an elementary proof for a regularity of the Rickart C*-algebra. He also gets a result about the completely additive measures on von Neumann algebras.

谐波分析的问题通常减少为翻译不变式操作员的邀请。作为此类运营商的有用的实际分析方法，有一个奇异的积分理论。但是，我们关注对该理论类别不满意的重要翻译不变的操作员。在那里，Kakeya最大功能起着重要的作用。 igari定义了具有特殊基础的最大功能，并给出了一个估算值，该估计值可以提供最佳的径向功能估计，也给出了部分波尔加因的结果。阿赖伊研究了和谐分析的观点，椭圆形的部分差异操作员，该操作员被重新纳入重新元素在边界中的所有点中，例如Stein歧管的伪convex域中的操作员以及带有theta结构的歧管中。他在此类运营商的和谐分析中获得了基本结果，并正在准备一篇论文。另外，他发现他有可能解决几个复杂变量功能的fatou问题。很长一段时间以来，研究了Navier-Strokes方程的独特性，但它仍然是一个未解决的主要主题。 Masuda引入了一种非常新的方法，这是解决此问题的真实可变方法，并找到了解决该问题的开始。在维罗纳举行的国际会议上报告了这一结果。此外，他解决了对二维复杂空间中恒定曲率最小表面分类的猜想，从与K.Kenmotsu的合作。基本证明，有Rickart C*-Algebra的规律性。他还对von Neumann代数的完全添加剂度量得到了结果。