2015 Fiscal Year Final Research Report
Research on Fourier integrals and singular integrals
| Project/Area Number |
25400130
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
Sato Shuichi 金沢大学, 学校教育系, 教授 (20162430)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | Fourier 級数 / 特異積分 |
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| Outline of Final Research Achievements |
We considered Littlewood-Paley operators and singular integral operators in general homogeneous groups including the Heisenberg group and proved that those operators have mapping properties similar to the ones that are known on the Euclidean spaces. Here, the kernels of the operators are assumed to have minimal size conditions and cancellation properties. Also, we have succeeded to characterize the Sobolev spaces on the Euclidean spaces by some Littlewood-Paley operators (IllinoisJ. Math. 58(4)).
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| Free Research Field |
解析学基礎
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