Harmonic Analysis for Some Orthogonal Expansions

一些正交展开的调和分析

基本信息

批准号：
13640160
负责人：
KANJIN Yuichi
金额：
$ 1.86万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640160/
关键词：
Hardy space Paley's inequality Hausdorff operator diffusion equation the self-adjoint Trotter-Kato product formula Marcinkiewicz integral Riccati differential equation Hardy's ineguality Paley's inequality Hausdorff operatol Raly's ine

项目摘要

Our research results are summarized as follows. The head investigator Kanjin has obtained Paley's inequality and Hardy's inequality with respect to the Jacobi expansions. The classical Peley's inequality and Hardy's inequality are two of the most familiar inequalities on the Fourier coefficients of functions in the Hardy space of certain analytic functions in the unit disc. The inequalities were originally proved by complex method. It is difficult to study orthogonal expansions by using complex method. Recent development of the real Hardy space theory, especially the atomic decomposition characterization or the real Hardy space and BMO space duality, allows to discuss problems on inequalities with respect to orthogonal expansions. Our Hardy's inequality have proved by applying the atomic decomposition to the Jacobi function system and Our Paley's inequality has gotten by using the real Hardy space and BMO space duality. Further, he has studied the Cesaro operator and, generally, the Hausdorff operator. The result says that the Hausdorff operator is bounded on the real Hardy space with parameter p smaller than one under some conditions.The investigator Tsuchiya has investigated convergence of Dirichlet forms of diffusion process without assuming that the underlying measures are fixed or compatible with a fixed one. Ichinose has obtained more results on the self-adjoint Trotter-Kate product formula with operator norm. Sato has considered Marcinkiewicz integrals arising from rough kernels satisfying LlogL condition on the unit (n-l)-sphere and proved the weak type (1,1) estimates. Tohge has studied a Riccati differential equation whose coefficient is expressible in terms of a special Weierstrass pe-function and shown that all the solutions are meromorphic.

我们的研究结果总结如下。主管汉金（Kanjin）在雅各比（Jacobi）的扩张方面获得了Paley的不平等和Hardy的不平等现象。经典的Peley的不平等和Hardy的不平等是在单位光盘中某些分析函数的功能傅立叶傅立叶系数上最熟悉的两个不平等。不平等最初是通过复杂方法证明的。使用复杂的方法很难研究正交扩展。真正的Hardy空间理论的最新发展，尤其是原子分解表征或真实的Hardy空间和BMO空间双重性，可以讨论有关正交扩张的不平等问题的问题。通过将原子分解应用于Jacobi功能系统，我们的Hardy的不平等已证明，我们的Paley的不平等已通过使用真实的Hardy空间和BMO空间双重性来获得。此外，他研究了切萨罗操作员，并且通常是豪斯多夫操作员。结果表明，在某些条件下，豪斯多夫操作员在实际的耐寒空间上，参数p小于一个。。 Ichinose在具有运算符规范的自动伴侣 - 凯特产品公式上获得了更多结果。佐藤（Sato）考虑了Marcinkiewicz积分，这些积分是由满足单元（n-l） - 球体上LLOGL条件的粗糙内核产生的，并证明了弱类型（1,1）的估计值。 Tohge研究了一个Riccati微分方程，该方程在特殊的WeierStrass PE功能方面表达了该系数，并表明所有溶液都是Meromororphic的。