2016 Fiscal Year Final Research Report
Structures of quasi-Banach function spaces and the theory of martingales
Project/Area Number |
25400129
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
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Research Institution | University of Toyama |
Principal Investigator |
Kikuchi Masato 富山大学, 大学院理工学研究部(理学), 教授 (20204836)
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Project Period (FY) |
2013-04-01 – 2017-03-31
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Keywords | マルチンゲール / マルチンゲール不等式 / Banach関数空間 / 準Banach関数空間 / 弱空間 |
Outline of Final Research Achievements |
We investigated some characterizations of a Banach function space X such that various martingale inequalities remain valid in the weak space w-X. A Banach function space is a function space which is a generalization of the well-known Lp-space, and the weak space of a Banach function space X is a quasi-Banach space associated with X, which is a generalization of the weak-Lp-space. As a result of our investigations, we could give characterizations of Banach function space X such that martingale inequalities such as of Burkholder-type and of Doob-type, and so on remain valid in w-X, and we could show that there is close connection between martingale theory and the structures of (quasi-)Banach function spaces.
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Free Research Field |
マルチンゲール理論,及び,関数空間論
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