2011 Fiscal Year Final Research Report
Theory of Singular Integral Operators in Non-commutative Harmonic Analysis. A verification of Use of Real Hardy Spaces.
| Project/Area Number |
20540188
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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)
J-PH. Anker Universite d' Orleas, Batiment de Mathematiques, 教授
K. Koufany l' Universite Henri Poincare, Nancy I, Professor
L. Peng 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
R. Daher University Hassan II, Faculty of Sciences, 教授
A. Abouelaz University Hassan II, Faculty of Science, 教授
M. Sifi Campus Universitaire, Faculty of Sciences of Tunis, 教授
M. Voit Univaerstat Dortmund, Fachbereich Mathematik, 教授
M. Rosler TU Clausthal, Department of Mathematics, 教授
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| Project Period (FY) |
2008 – 2011
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| Keywords | 非可換調和解析 / 実ハーディ空間 / ヤコビ解析 / 最大関数 / 特異積分 / L^p有界性 / アトム分解 / 補間法 |
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| Research Abstract |
In the past 4 years from 2008 to 2011 real Hardy spaces for Jacobi analysis and their atomic decompositions have been investigated. Moreover, as applications of the Hardy spaces, Lp boundedness of some singular integral operators and the theory of interpolation spaces were established. These results for the spaces of non-homogeneous type are natural extension of ones in the Euclidean spaces and the Dunkl analysis,. Jacobi analysis is a special case of Chebli-Trimeche hypergroups. As ancillary research, several uncertainty principles are also obtained for the spaces of non-homogeneous type. These results obtained in this research pave the way to harmonic analysis for the Cherednik transform.
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