2002 Fiscal Year Final Research Report Summary
Research on Fourier integrals of several variables
| Project/Area Number |
13640159
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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 |
Basic analysis
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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) |
KANJIN Yuichi Kanazawa Univ. Faculty of Faculty of Engineering, professor, 工学部, 教授 (50091674)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Littlewood-Paley functions / rough operators / transference / multilinear operators / weak (1,1) estimates / singular integrals |
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| Research Abstract |
(1) We proved the weighted weak type (1,1) estimates both for the Calderon-Zygmund type singular integrals and for the Littlewood-Paley functions. These operators are defined by certain rough kernels.
(2) We proved some weighted estimates for the Littlewood-Paley functions on the weighted Hardy spaces. Also some weighted estimates for the generalized Bochner-Riesz operators and for the generalized spherical means are obtained.
(3) For certain classes of pseudo-differential operators, we proved L^2_w - L^2_w, L^1_w - L^<1,∽>_w and H^1_w - L^1_w estimates.
(4) We proved the L^p estimates for certain singular integrals associated to the variable surface of revolution.
(5) We studied certain multilinear Littlewood-Paley functions arising from rough kernels.
(6) We proved the weak type (1,1) estimates for the Marcinkiewicz integrals by assuming for the kernel the LlogL condition on the unit sphere S^<n-1>.
(7) We proved transference theorems between the multilinear multiplier operators on the Euclid space R^n and the ones on the torus T^n. Also we obtained some applications of these results.
(8) We proved transference theorems for the L^p, the weak L^p and H^p - L^p estimates between the Littlewood-Paley functions on the Euclid space R^n and those on the torus T^n. Also we obtained some applications of these results.
(9) We proved the L^p estimates for the Littlewood-Paley functions along curves and the related singular integrals, both arising from the rough kernels. As applications, we proved the L^p estimates for the Marcinkiewicz integrals along curves and the singular integrals associated to the surface of revolution, both with H^1 kernels.
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