2003 Fiscal Year Final Research Report Summary
On the research of some applications in real analysis for the Lorentz and Orlicz spaces
| Project/Area Number |
12640185
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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 | Kagoshima University |
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Principal Investigator |
KITA Hiro-o Kagoshima University, Faculty of Education, Professor, 教育学部, 教授 (20224941)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Naganori Oita University, Faculty of Education and Welfare Science, Professor, 教育福祉科学部, 教授 (40040737)
KEMOTO Nobuyuki Oita University, Faculty of Education and Welfare Science, Professor, 教育福祉科学部, 教授 (70161825)
YASUI Tsutomu Kagoshima University, Faculty of Education, Professor, 教育学部, 教授 (60033891)
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| Project Period (FY) |
2000 – 2003
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| Keywords | Oelicz space / weight / Hardy / transfer map / embedding / product space / control function / normality |
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| Research Abstract |
The first research product of our study is as follows. We obtained some weighted norm inequalities for the Hardy-Littlewood maximal function M(f) and the iterated maximal function M^k(f) = M(M^<k-1>(f)) in Orlicz spaces. Let L^Φ_ω(R^n) be a weighted Orlicz space with weight ω, where Φ is a Young function. We could a necessarily and sufficient condition for the weighted inequality for the maximal function in weighted Orlicz spaces.
Our second research product is a study of the control function of almost everywhere convergence of functions. We introduced a new concept of modular function space which is a generalization of Banach function space. We could decide this control function for almost everywhere convergence of the functions in modular function spaces.
Yasui studied relations between Haefliger's obstructions to topological embeddings and transfer maps. He proved that vanishing Haefliger's obstructions of a map means that the map is cobordant to a differentiable embedding in the sense of Stong.
On the computation of high accuracy of the expected values of products of the normal order statistics. Mori showed by the numerical method that Gaussian method is highly accurate and very efficient on reducing the number of iterative calculations as possible as we can.
Kemoto investigated the preservation of mild normality and strong zero-dimensionality of products of ordinals. He showed that the product of two subspaces of an ordinal is mildly normal and that the product of finitely many subspaces of an ordinal is strongly zero-dimensional.
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Research Products
(10 results)
