| Project/Area Number |
10440046
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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 | KWANSEI GAKUIN UNIVERSITY (1999-2000)
Nara Women's University (1998) |
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Principal Investigator |
YABUTA Kozo Kwansei Gakuin Univ., School of Science, Professor, 理学部, 教授 (30004435)
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| Co-Investigator(Kenkyū-buntansha) |
KANJIN Yuichi Kanazawa University, Fuculty of Engineering, Professor, 工学部, 教授 (50091674)
MIYACHI Akihiko Tokyo Woman's Christian University, Faculty of Cultures and Science, Professor, 文理学部, 教授 (60107696)
SAKA Koichi Akita University, Faculty of Technology and Resorces, Professor, 工学資源学部, 教授 (20006597)
NAKAJI Takahiko Hokkaido University, Graduate School of Science, Professor, 理学研究科, 教授 (30002174)
YONEDA Kaoru Osaka Prefectural University, Department of Integrated Sciences, Professor, 総合科学部, 教授 (80079029)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥11,000,000 (Direct Cost: ¥11,000,000)
Fiscal Year 2000: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 1999: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1998: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | singular integrals / L^p space / Hardy spaces / weighted inequalities / 実解析 / 最大関数 |
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| Research Abstract |
(1) Singular integrals with Calderon-Zygmund type kernels and with rough kernels
(i) A_1 weighted weak (1,1) estimates for oscillatory singular integrals with Calderon-Zygmund kernels. A_p (p>1) case is known. We have overcomed the difficulties in the case p=1.
(ii) Let Tf (x) = ∫K (x, y) f (y) dy. It is known that T is bounded from the Hardy space H^p to the local Hardy space h^p, under the condition T1 = 0. We could show that under more weak condition, Lipscitz condition, the same result holds. A counterexample was given in the critical index case.
(2) Vector valued singular integrals and Littlewood-Paley theory
New results on the boundedness of parametrized Marcinkiewicz integrals in L^p, Lipschitz, and Campanato spaces, which correspond to Littlewood-Paley's g-functions, g^*_λ-functions and Lusin's area integral. Using this and a recent result on multilinear Calderon- Zygmund singular integrals, we have an interesting result on multilinearized Littlewood-Paley operators.
(3) Fractional integrals.
We have generalized the notion of fractional integrals and studied those properties in several function spaces, such as L^p, BMO, Lipschitz, Campanato, and Morrey spaces, Orlicz spaces.
(4) Singlular integrals and Hardy spaces of discrete type.
We have molecular characterization of discrete Hardy space, and using this, we have given a theorem of fractional integrals and multiplier theorem of Marcinkiewicz type. Also, generalized discrete Hilbert transform were formulated and its weak l^1 boundedness were given.
(5) Almost everywhere convergence results.
New function space, modular function space, were introduced, and its effectiveness were studied
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