权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Harmonic Analysis on Orthogonal Expansions

正交展开式的调和分析

基本信息

批准号：
10640155
负责人：
KANJIN Yuichi
金额：
$ 1.28万
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：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640155/
关键词：
Hardy space Hardy's inequality Lie-Trotter-Kato product formula Nevanlinna theory diffusion equation oscillatory singular integrals Hardy Space tranceterenee therem 拡散方程式境界値問題ネヴァンリンナ理論 rough operator weak type estimate Hardy's

项目摘要

Our research results are summarized as follows. Head investigator Kanjin has obtained Hardy's inequalities with respect to the Hermite and Laguerre expansions. The classical Hardy's inequality is a well-known inequality on the Fourier coefficients of functions in the Hardy space of certain analytic functions in the unit disc. The inequality was originally proved by complex method. It is difficult to study the orthogonal polynomial expansions by using complex method. Recent development of the real Hardy space theory, especially the atomic decomposition characterization of the real Hardy space allows to discuss the problem on the inequalities with respect to the orthogonal expansions. Our inequalities have proved by applying the atomic decomposition to the Hermite and Laguerre systems. By our method we have also gotten Hardy's inequality for the Hankel transforms. Further, we have studied the discrete Hardy space and obtained the molecular characterization of the space. As its applications, we have proved the theorem of fractional integration and the Marcinkiewicz type multiplier theorem for the discrete Hardy space.Investigator Ichinose has proved the Lie-Trotter-Kato product formula with operator norm. Tohge has gotten a result on the relation between the classical Nevanlinna theory and linear differential equations. Tsuchiya has shown Feller property for a Markov process obtained by superposing two diffusion processes in two domains under Holder condition for coefficients. Sato has considered Al-weights and proved weighted weak type (1,1) estimates for oscillatory singular integrals with kernels satisfying a Dini condition.

我们的研究结果总结如下。首席研究员Kanjin已经得到了关于Hermite和Laguerre展开的Hardy不等式。经典的哈代不等式是关于单位圆盘上某些解析函数在哈代空间中的傅里叶系数的一个众所周知的不等式。该不等式最初是用复数方法证明的。用复形法研究正交多项式展开是困难的。实Hardy空间理论的最新发展，特别是实Hardy空间的原子分解刻划，使得讨论正交展开下的不等式问题成为可能。我们的不等式已经通过将原子分解应用到Hermite和Laguerre系统得到了证明。用我们的方法也得到了汉克尔变换的哈代不等式。进一步研究了离散Hardy空间，得到了该空间的分子表征。作为它的应用，我们证明了离散Hardy空间的分数阶积分定理和Marcinkiewicz型乘子定理。研究者一濑用算子范数证明了Lie-Trotter-Kato产品的配方。Tohge得到了经典奈万林纳理论与线性微分方程之间关系的结果。土屋给出了在系数的Holder条件下，在两个域内叠加两个扩散过程得到的马尔可夫过程的Feller性质。Sato考虑了al权，并证明了核满足Dini条件的振荡奇异积分的加权弱型（1,1）估计。