| Project/Area Number |
24540191
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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 | Keio University |
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Principal Investigator |
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| Research Collaborator |
NAKAI Eiichi 茨城大学, 理学部, 教授 (60259900)
MIYACHI Akihiko 東京女子大学, 現代教養学部, 教授 (60107696)
Anker J-Ph. Universite d'Orleas, Bâtiment de Mathématiques, 教授
Koufany K. Universite de Lorraine, 教授
Peng L. 北京大学, 数学科学学院, 教授
Lie Heping 北京大学, 数学科学学院, 教授
Lie Jianming 北京大学, 数学科学学院, 助教授
Daher R. University Hassan II, Faculty of Sciences, 教授
Abouelaz A. University Hassan II, Faculty of Science, 教授
Mejjaoli H. King Faisal University, College of Science, 教授
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 調和解析 / 非可換調和解析 / ヤコビ変換 / hypergroup / ハーディ空間 / アーベル変換 / ヤコビ解析 / 特異積分論 / 特異積分作用素 / 有界性 / Kunze-Stein 現象 / 実ハーディ空間 / 特異積分 / 離散ラドン変換 / 逆変換公式 / 補間理論 / Kunze-Stein現象 / 国際研究者交流 / 中国：モロッコ：フランス |
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| Outline of Final Research Achievements |
As a target of non-commutative harmonic analysis, mainly, on the Jacobi hyper-group, we investigate (H1,L1) boundedness of maximal functions, Littlewood-Paley's function and Lusin's area function and the Kunze-Stein phenomenon. In conventional approach, we have used the Jacobi transform and its inverse. However, in this research, we use the Abel transform and its inverse. As for maximal functions and Littlewood-Paley's function, we can obtain (H1,L1) boundedness, however, for Lusin's area function we have to modify the function to deduce (H1,L1) boundedness. Although the endpoint estimate of the Kunze-Stein phenomenon was already known, by using the present method, we can give an alternative proof.
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