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

1.研究了开单位圆盘上有界解析函数空间H∞上复合算子的性质. T.细川，K. J. Izuchi和作者刻画了H∞上加权复合算子集的拓扑结构，并发表了一篇论文。本文继续研究了H∞空间上复合算子的线性组合，在系数为正的情况下，完全刻画了其紧性，并估计了其本质范数。Izuchi和他推广了这些结果，得到了使得系数的真实的部分为正的本质范数的估计，并给出了结果。2. K. J. Izuchi和作者刻画了开单位圆盘上有界调和函数空间上Hankel型算子的紧性和完全连续性，并发表了.这些算子与紧一致代数、Dunford-Pettis性质和Bourgain代数有关。此外，作者还研究了 ...更多信息 哈代和伯格曼空间，并在RIMS联合研究“解析函数空间及其运算符”（2006年6月21日（星期三）- 23日（星期五），京都大学数学科学研究所）的谈话。本次会议是作者与本项目有关的申请，并被接受。3. T. Hosokawa和作者研究了Bloch空间上复合算子空间的拓扑结构，并发表了算子拓扑学。进一步讨论了两个复合算子差在Bloch空间和小Bloch空间上的有界性和紧性，证明了小Bloch空间上的差的弱紧性等价于紧性.这篇论文也被接受了。4. Hibschweiler和Portnoy在哈代空间和加权Bergman空间上定义了复合算子和微分算子的乘积，并利用Carleson型测度研究了加权Bergman空间之间的有界性和紧性.但是这样的加权Bergman空间在刻画复合算子和微分算子的乘积的有界性和紧性时不包括哈代空间的情形。作者对此问题进行了研究并发表了论文。少

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