1986 Fiscal Year Final Research Report Summary
Studies of Harmonic Analysis
| Project/Area Number |
60460003
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
IGARI Satoru Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (50004289)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Shuichi Faculty of Sciences, To"hoku University Assistant, 理学部, 助手 (20162430)
OKADA Masami Faculty of Sciences, To"hoku University Lecturer, 理学部, 講師 (00152314)
HOTTA Tyoshi Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (70028190)
KATO Junji Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (80004290)
MASUDA Kyuya Faculty of Sciences, To"hoku University Professor, 理学部, 教授 (10090523)
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| Project Period (FY) |
1985 – 1986
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| Keywords | Harmonic function / subharmonic function / Hardy space / Operator algebra / Evolution equation / Semi-simple group / D-module / 補間定理 |
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| Research Abstract |
Classical harmonic analysis has been a considerable flowering duaring the past 15 years starting from the results due to Fefferman-Stein,Carleson and others. The object of our program was to study the idea of classical harmonic analysis and to develop it in various fields in mathematics by the coorperative research with several specialists in our institute.An extract of our results is the following :
1. An interpolation theorem of operators on a product measure space is shown. As applications we solved partially a problem on Riesz-Bochner means and on Kakeya's maximal function. Hardy spaces on a product space are investigated with connection to holomorphic functions of two variables.We are now generalizing classical Hardy space theory to a manifold of negative curvature.
2. We have studied non-linear evolution equations getting several results on a property of the solutions of Navier-Stokes equation near t = 0, existence of global solutions and analiticity of solutions.
3. By a method of D-modules it is succeeded to analyse and classify the singularities of characters through Harish-Chandra's differential equation. We have a program to develop these researches in future.
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