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Researches on the Spaces of Analytic and Harmonic Functions and Their Operators

解析函数、调和函数空间及其算子的研究

基本信息

批准号：
17540169
负责人：
OHNO Shuichi
金额：
$ 1.28万
依托单位：
Nippon Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540169/
关键词：
Hardy spaces Bergman spaces Bloch spaces composition operator weighted composition operator Hankel-type operator boundedness compactness 微分作用素

项目摘要

1. We have investigated properties of composition operators on the space H∞ of bounded analytic functions on the open unit disk. T. Hosokawa, K. J. Izuchi and the author characterized the topological structure of the set of weighted composition operators on H∞ and published a paper. The author has continued to study linear combinations of composition operators on the space H∞ and completely characterized the compactness and estimated the essential norms in the case that coefficients are positive. And Izuchi and he extended these results and obtained the estimation of the essential norms such that real parts of coefficients are positive and submitted results. 2. K.J. Izuchi and the author characterized the compactness and complete continuity of Hankel-type operators on the space of bounded harmonic functions on the open unit disk and published. These operators related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras. Moreover the author studied the cases of … More Hardy and Bergman spaces and had a talk at RIMS Joint Research "Analytic Function Spaces and Their Operators" (June 21(Wed) - 23(Fri), 2006,Kyoto University Research Institute for Mathematical Science). This conference was applied by the author with the relation ship to this project and accepted. 3. T. Hosokawa and the author studied the topological structure of the space of composition operators on the Bloch space in the operator topology and published. Furthermore we considered the boundedness and the compactness of the differences of two composition operators on the Bloch and the little Bloch spaces and proved that the weak compactness of the differences on the little Bloch space is equivalent to the compactness. This paper also is accepted. 4. Hibschweiler and Portnoy defined the products of composition and differentiation operators on Hardy and weighted Bergman spaces and investigated the boundedness and the compactness between weighted Bergman spaces using the Carleson-type measures. But such weighted Bergman spaces would not include the Hardy space case in the characterization of boundedness and compactness of the products of composition and differentiation operators. The author studied this problem and published. Less

1.我们研究了开单位圆盘上有界解析函数的空间H∞上的复合算子的性质。 T. Hosokawa、K. J. Izuchi 等作者表征了 H∞ 上的加权合成算子集合的拓扑结构，并发表了论文。作者继续研究空间H∞上复合算子的线性组合，完整地表征了系数为正情况下的紧性并估计了本质范数。 Izuchi 和他扩展了这些结果，得到了使系数实部为正的基本范数的估计，并提交了结果。 2. K.J. Izuchi 和作者描述了开单位圆盘上有界调和函数空间上 Hankel 型算子的紧致性和完全连续性并发表。这些运算符与紧一致代数、邓福德-佩蒂斯性质和布尔干代数相关。此外，作者还研究了Hardy和Bergman空间的案例，并在RIMS联合研究中心做了报告“Analytic Function Spaces and Their Operators”（2006年6月21日（周三）-23日（周五），京都大学数学科学研究所）。本次会议是由与本项目有关系的作者提出申请并被接受的。 3. T. Hosokawa和作者研究了算子拓扑中布洛赫空间上复合算子空间的拓扑结构并发表。进一步考虑了布洛赫空间和小布洛赫空间上两个复合算子差的有界性和紧性，证明了小布洛赫空间上差的弱紧性与紧性等价。这篇论文也被接受了。 4. Hibschweiler 和 Portnoy 定义了 Hardy 和加权 Bergman 空间上的复合算子和微分算子的乘积，并使用 Carleson 型测度研究了加权 Bergman 空间之间的有界性和紧性。但这种加权伯格曼空间在描述合成算子和微分算子的乘积的有界性和紧致性时不包括哈代空间情况。作者研究了这个问题并发表了。较少的