Structures of Banach function spaces that are derived from the theory of martingales
| Project/Area Number |
20540160
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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 | University of Toyama |
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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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| Co-Investigator(Renkei-kenkyūsha) |
IZUMISAWA Masataka 東海大学, 理学部, 教授 (50108445)
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| Project Period (FY) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | マルチンゲール / Banach関数空間 / 再配列不変空間 / Boyd指数 / ノルム不等式 / 再配分不変空間 / Boyd index / 再配置不変空間 / マルチンゲール変換 / マルチンゲール不等式 / 再配分(再配列)不変空間 / マルチングール |
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| Research Abstract |
As a consequence of this research, we obtained a lot of theorems which show that we can analyze some structures of Banach function spaces by using martingale theory. For example we proved that, when X is a Banach function space, somenecessary and sufficient conditions which ensure that certain kinds of martingaleinequalities are valid in X can be expressed in terms of the rearrangement-invariance of X and the Boyd indices of X. This result shows that there are close connections between the validity of martingale inequalities and the structures of Banach function spaces.
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Report
(7 results)
Research Products
(27 results)
