| 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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| 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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