1998 Fiscal Year Final Research Report Summary
Research on Fourier integrals of several variables
| Project/Area Number |
09640168
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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 |
解析学
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| Research Institution | Kanazawa University |
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Principal Investigator |
SATO Shuichi Kanazawa Univ., Faculty of Education, associate professor, 教育学部, 助教授 (20162430)
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| Co-Investigator(Kenkyū-buntansha) |
TOHGE Kazuya Kanazawa Univ., Faculty of Faculty of Engineering, associate professor, 工学部, 助教授 (30260558)
KANJIN Yuichi Kanazawa Univ., Faculty of Faculty of Engineering, professor, 工学部, 教授 (50091674)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Rough operators / Square functions / Littlewood-Paley theory / Hardy's inequality / Nevanlinna theory / meromorphic function |
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| Research Abstract |
(1)We proved the pointwise relations between some multiparameter square functions on R^n, and we applied them to prove H^p - L^p and L(log L)^<n-1> - L^<1, *> estimates for multiparameter Marcinkiewicz integrals. To show the weak type estimate, we also proved a resonance theorem on Orlicz spaces.
(2)We proved that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on L^p_ 1 <p < *, w * A_p (the weights of Muckenhoupt). The kernels are satisfying only size and cancellation conditions. Then, we gave some applications to the Carleson measures on the upper half space.
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