2012 Fiscal Year Final Research Report
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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| Keywords | マルチンゲール / Banach関数空間 / 再配列不変空間 / Boyd指数 |
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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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Research Products
(12 results)
