2019 Fiscal Year Final Research Report
Research on Fourier integrals and singular interals
| Project/Area Number |
16K05195
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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) |
2016-04-01 – 2020-03-31
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| Keywords | singular integrals / square functions / Hardy spaces / Sobolev spaces |
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| Outline of Final Research Achievements |
We considered singular integrals on homogeneous groups including Heisenberg groups and established weak type estimates on the weighted Lebesgue spaces. The kernel of the singular integral is assumed to have no regularity and only a size condition and cancelation were assumed. Characterizations of Hardy spaces on homogeneous groups and some Sobolev spaces were obtained in terms of Littlewood-Paley functions and Lusin area integrals.
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| Free Research Field |
調和解析, Fourier 解析
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| Academic Significance and Societal Importance of the Research Achievements |
ある種の特異積分作用素を考えて, その荷重 Lebesgue 空間上での弱有界性が示された. ここで, 特異積分作用素には滑らかさの正則性が仮定されていなく, サイズに関する最小の仮定と cancellation に関する仮定が置かれているのみである. Littlewood-Paley 関数, Lusinの面積積分により斉次群上のHardy 空間の特徴づけ, ある種のSobolev 空間の特徴づけが得られた.
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