THE RESEARCH OF OPERATORS ON LORENTZ SPACES BY THE METHOD OF HARMONIC ANALYSIS

调和分析法研究洛伦兹空间算子

• 批准号: 16540134
• 负责人: SATO Enji
• 金额: $ 2.24万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540134/
• 关键词: Jacobi orthonormal system; Hankel transformation; deficiency; Morrey space; Julia set; chaotic map; Mobious transformation; transplatation; ネヴアンリンナ理論; 複素力学系; 移植作用素

Our purpose of this research is to study the properties of operators on Lorentz spaces by the method of haomonic analysis. Our investigations did the research at each special point. The content is as follows :Sato studied the relation between some operators of Hankel transforms and the operators of Jacobi orthgonal system on (0,pi). Also he studied an inequality related to the operators on the Lorentz-Zygmund spaces. Mori researched about a problem of constructions of algebraically nondegenereate meromorophic mappings and the uniquness problem related to meromorphic functions. Mizuhara showed the weak factorization theorem of H^1-functions due to generalized Morrey functions, blocks and the Riesz potential. Also applying this result, he observed the necessity for which the commutator between the Reisz potential and a locally integrable function to be bounded on the generalized Morrey spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. He studied conjugacy of new type connecting two chaotic maps. Sekigawa studied the M"obious transformations on the high dimensional Euclidean spaces, by using Clifford matrix representations of M"obious transformations. Kanjin showed the boundedness of the transplantation operators concerning the Hankel transform on the Hardy spaces. Also he showed the boundedness of Cesaro operators, and Hardy's inequality related to the Fourier coefficients with respect to the Jacobi series on the Hardy's space.

本文的目的是利用混沌分析的方法研究Lorentz空间上算子的性质。我们的调查在每一个特殊的点上做了研究。研究了（0，pi）上Hankel变换的某些算子与Jacobi正交系的算子之间的关系。此外，他研究了一个不平等有关的运营商的洛伦兹-Zygmund空间。Mori研究了代数非退化亚纯映射的一个构造问题和与亚纯函数有关的唯一性问题。Mizuhara证明了H^1-函数的弱分解定理，这是由于广义Morrey函数，块和Riesz势。还应用这一结果，他观察到的必要性，其中换向器之间的Reisz潜在的和一个局部可积的功能是有界的广义Morrey空间。中田研究了一些几何性质的朱莉娅集有理函数的黎曼领域。Kawamura讨论了关于测度空间上与混沌映射相关的概率密度函数行为的理论的推广。他研究了连接两个混沌映射的新型共轭性。关川用M“obious变换的Clifford矩阵表示研究了高维欧氏空间上的M“obious变换。Kanjin证明了Hankel变换的移植算子在哈代空间上的有界性。此外，他表明有界的塞萨罗运营商，和哈代的不等式有关的傅立叶系数就雅可比系列的哈代的空间。

项目成果

A transplantation theorem for the Hankel transform on the Hardy space

Hardy空间上Hankel变换的移植定理

• 期刊: Tohoku Math.J (印刷中)
• 作者: T.Ichinose;D.Fan;G.G.Gundersen;佐藤 秀一;G.G.Gundersen;Y.Kanjin
• 通讯作者: Y.Kanjin

Deficiencies of meromorophic mappings for hypersurfaces

超曲面亚形映射的缺陷

• 发表时间: 2005
• 期刊: J. of Mathematical Society of Japan 57
• 作者: Yoshihiro Aihara;Seiki Mori
• 通讯作者: Seiki Mori

Meromorophic mappings and deficiencies

亚形映射和缺陷

• 发表时间: 2004
• 期刊: Advanced Studies in Pure Mathematics, Complex Analysis in Several Variables, Math.Soc.of Japan
• 作者: Weiling Xiong;Weichuan Lin;Seiki Mori;Shinzo Kawamura;Yuichi Kanjin;Yuichi Kanjin;Seiki Mori
• 通讯作者: Seiki Mori

Uniqueness of meromorphic of functions

函数亚纯的唯一性

• 发表时间: 2006
• 期刊: Scientiae Mathematicae Japonicae 62
• 作者: W.Xiong (with W.Lin;S.Mori)
• 通讯作者: S.Mori)

Factarization of functions in H1(Rn) and generalized Morrey spaces

H1(Rn) 和广义 Morrey 空间中函数的分解

• 期刊: Math. Nachr. (to appear in)
• 作者: Yasuo Komori;Takahiro Mizuhara
• 通讯作者: Takahiro Mizuhara