2013 Fiscal Year Final Research Report
Analysis of Cesaro-type integral operators via function-theoretic properties of symbol functions
| Project/Area Number |
23740100
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | ベルグマン空間 / チェザロ型積分作用素 / 合成作用素 / 荷重合成作用素 / フォック空間 / Carleson測度 / Zygmund F-algebra |
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| Research Abstract |
In this research, we considered the Bergman spaces which consist of holomorphic functions on the unit disk or the unit ball and integral type operators, composition operators and weighted composition operators acting on these spaces. Our purposes are to characterize operator-theoretic properties of these operators via function-theoretic properties of symbol functions and self-maps. Furthermore we will estimate the operator norm and the essential norm for these type operators by Berezin-type transforms.
Also we introduced the Zygmund F-algebra which consists of holomorphic functions. This function space contains all Bergman spaces and Nevanlinna type spaces. We investigated the structure of linear isometries or multiplicative isometries on the Zygmund F-algebra.
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