2006 Fiscal Year Final Research Report Summary
Researches on the Spaces of Analytic and Harmonic Functions and Their Operators
| Project/Area Number |
17540169
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Nippon Institute of Technology |
|---|
Principal Investigator |
OHNO Shuichi Nippon Institute of Technology, Department of Technology, Associate Professor, 工学部, 助教授 (20265367)
|
|---|
| Project Period (FY) |
2005 – 2006
|
| Keywords | Hardy spaces / Bergman spaces / Bloch spaces / composition operator / weighted composition operator / Hankel-type operator / boundedness / compactness |
|---|
| Research Abstract |
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
|
Research Products
(9 results)
