| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
We considered Littlewood-Paley operators and singular integral operators in general homogeneous groups including the Heisenberg group and proved that those operators have mapping properties similar to the ones that are known on the Euclidean spaces. Here, the kernels of the operators are assumed to have minimal size conditions and cancellation properties. Also, we have succeeded to characterize the Sobolev spaces on the Euclidean spaces by some Littlewood-Paley operators (IllinoisJ. Math. 58(4)).
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