| Project/Area Number |
17540154
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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 Faculty of Education, associate professor, 教育学部, 助教授 (20162430)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Radon singular integral / extrapolation / rough kernel / 特異積分 |
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| Research Abstract |
(1) We consider certain non-regular pseudo-differential operators T_σ and study the question of their boundedness on the weighted Triebel-Lizorkin and Besov spaces. In particular, we substantially relax the regularity condition on the symbol σ due to Bourdaud for T to be bounded on the Sobolev spaces H^s_p.
(2) We prove the Lp boundedness of the singular integral operators associated with a variable surface of revolution assuming the boundedness of related lower dimensional maximal operators. The singular integrals are defined by rough kernels satisfying certain size and cancellation conditions. As an application, we extend a result of Grafakos-Stefanov and Fan-Guo-Pan to the case of a singular integral of R. Fefferman type of two variables.
(3) We study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove Lp boundedness of the singular integrals under a certain sharp size condition on their kernels.
(4) We prove certain Lp estimates (1<p<∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels with generalized homogeneity. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals and implies the Stein-Wainger estimate for a trigonometric integral involving a phase function defined by a curve that does not lie in an affine hyperplane.
(5) We consider a singular integral along a manifold of finite type. We prove a sharp Lp estimate for the singular integral operator according to a size condition of its kernel, which is useful in applying an extrapolation method.
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