New development in non-commutative harmonic analysis related to singular integrals - A fusion of representation theory and real analysis

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540191
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Keio University
• Principal Investigator: KAWAZOE Takeshi 慶應義塾大学, 総合政策学部, 教授 (90152959)
• 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
• Project Period (FY): 2012-04-01 – 2016-03-31
• 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

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.

Free Research Field

調和解析