2001 Fiscal Year Final Research Report Summary
Study of harmonic analysis and applications to partial differential equations
| Project/Area Number |
11440037
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | The University of Tokyo |
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Principal Investigator |
ARAI Hitoshi The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (10175953)
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| Co-Investigator(Kenkyū-buntansha) |
KANJIN Yuichi Kanazawa University, Faculty of Sciences, Professor, 工学部, 教授 (50091674)
OZAWA Toru Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (70204196)
YAJIMA Kenji The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (80011758)
MORITO Shinya Nara women's University, Faculty of Sciences, lecturer, 理学部, 講師 (30273832)
NOGUCHI Junjiro The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20033920)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Harmonic functions / Negatively curved manifolds / Schrodinger equations / Nonlinear Schrodinger equations / Hardy spaces / Fourier multiplier / F.B.I transform / Bloch function |
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| Research Abstract |
Arai studied harmonic analysis on negatively curved manifolds. Let M be a complete, simply connected Riemannian manifold whose sectional curvatures K_M satisfy -∞ < -k^2_2 【less than or equal】 K_M 【less than or equal】 -k^2_1 < 0, where k_1 and k_2 are positive constants. Arai obtained several results on elliptic harmonic functions on M. In particular he established fundamental part of harmonic analysis on M by proving theorems related to Hardy spaces, BMO, VMO, Carleson measures, Green's potential. As applications, he also studied Bloch function theory on manifolds and the regularity problem of degenerate harmonic measures. Ozawa studied by using real variable method nonlinear Schrodinger equations, nonlinear wave equations and nonlinear Krein-Gordon equations. Yajima obtained some results on the fundamental solutions of Schrodinger equations. Kanjin proved Paley's inequality for Jacobi expansions and studied the Hausdorff operator acting on real Hardy spaces.
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