2011 Fiscal Year Final Research Report
Research on Fourier integrals of several variables
| Project/Area Number |
21540171
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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 金沢大学, 学校教育系, 准教授 (20162430)
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| Project Period (FY) |
2009 – 2011
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| Keywords | Fourier級数 / 特異積分 |
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| Research Abstract |
Weak type(1, 1) estimates were proved for 2-dimensional parabolic singular integrals defined by rough kernels which are homogeneous with respect to certain nonisotropic dilations, under the minimal size condition of the kernels. Some weighted mixed norm inequalities were proved for Hardy-Littlewood maximal operators, Hilbert transforms and maximal Hilbert transforms along homogeneous curves defined by certain nonisotropic dilations in the n-dimensional Euclidean space.
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