2002 Fiscal Year Final Research Report Summary
Research on the multi-linear harmonic analysis
| Project/Area Number |
13640147
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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 | Hokkaido University |
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Principal Investigator |
TACHIZAWA Kazuya Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (80227090)
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| Co-Investigator(Kenkyū-buntansha) |
OZAWA Tohru Hokkaido Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (70204196)
NAKAZI Takahiko Hokkaido Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (30002174)
HAYASHI Mikihiro Hokkaido Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40007828)
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| Project Period (FY) |
2001 – 2002
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| Keywords | ψ-transform / Schrodinger operator / eigenvalues |
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| Research Abstract |
In this research we studied about the characterization of weighted function spaces by means of the ψ-transform of Frazier and Jawerth and its appilications to partial differential operators. We proved a generalization of the Lieb-Thirring inequality which gives an estimate of the moments of the negative eigenvalues of the Schrodinger operator with negative potentials. Our result is about higher order degenerate elliptic operators. We gave a generalization of Egorov-Kondrat'ev's result.
We also proved a generalization of the Sobolev-Lieb-Thirring inequality. Our result is a weighted version of the original one, which is a generalization of Ghidaglia-Marion-Temam's theorem or Edmunds-Ilyin's theorem. Our results are expected to be applied to the estimate of the Hausdorff dimension of the attractor of nonlinear partial differential operators.
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