2019 Fiscal Year Final Research Report
Multilinear harmonic analysis and the singularity
| Project/Area Number |
16K05201
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 多重線形作用素 / 擬微分作用素 / フーリエ乗法作用素 |
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| Outline of Final Research Achievements |
In the field of harmonic analysis, the research to extend the theory for linear operators to the one for multilinear operators has been actively studied since around 2000. Nowadays this topic is often called multilinear harmonic analysis. Multilinear harmonic analysis is not just a generalization of linear theory, it is also a challenging problem for harmonic analysis, and it has the potential for the development of the study of partial differential equations from an application perspective. I studied how to approach operators with strong singularity such as bilinear Hilbert transform. I also obtained the results on the boundedness of bilinear pseudo-differential operators.
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| Free Research Field |
実解析学
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| Academic Significance and Societal Importance of the Research Achievements |
宮地晶彦氏(東京女子大学)との双線形擬微分作用素に関する研究は，V. Naibo 氏と A. Thomsom 氏の J. Math. Anal. Appl. (2019) の論文の中で，基本的な枠組みにおける有界性問題を終わらせたと紹介されており，価値あるものと信じている．また，L. Grafakos 氏，宮地晶彦氏との多重線形フーリエ乗法作用素の共同研究では，有界性を保証するためのマルチプライヤーに課すべき最適な正則性条件を決定することに成功した．
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