Application for the Kakeya problem in Harmonic Analysis
| Project/Area Number |
15K17551
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Nihon University (2017)
Kogakuin University (2015-2016) |
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Principal Investigator |
SAITO Hiroki 日本大学, 理工学部, 助教 (20736631)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 掛谷問題 / 極大関数 / 調和解析 |
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| Outline of Final Research Achievements |
The purpose of this study is to investigate the weighted estimate for the Kakeya maximal oeprator and to find a new technique and contribution for the Kakeya problem. The research from 2015 to 2017, we prove the boundedness of the weighted Kakeya maximal operator in general dimensional space assuming underlying weights belong to the reverse Holder classes. This result is a generalization of Wolff's range in 1995.
Further, we generalized the Hausdorff content to the non-additive measure defined on the abstract dyadic cubes and prove the boundedness of the Hardy-Littlewood maximal operator. Finally, we investigate the weighted estimate for strong maximal operator and prove the Fefferman-Stein type inequality with an arbitrary weight.
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Report
(4 results)
Research Products
(17 results)
