| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| 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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