1997 Fiscal Year Final Research Report Summary
Convergence Problems and Integral Inequalities
| Project/Area Number |
07640241
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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 |
解析学
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| Research Institution | Tohoku Gakuin University |
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Principal Investigator |
WATARI Chinami Tohoku Gakuin University, Faculty of Liberal Arts, Professor, 教養学部, 教授 (80004274)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAGAWA Kiyokazu Tohoku Gakuin University, Faculty of Liberal Arts, Associate Professor, 教養学部, 助教授 (80128884)
SEKIGUCHI Takeshi Tohoku Gakuin University, Faculty of Liberal Arts, Professor, 教養学部, 教授 (30004485)
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| Project Period (FY) |
1995 – 1997
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| Keywords | Bernstein inequality / BMO / Absolute convergence / DIGITAL SUM / 拡散移流型方程式 |
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| Research Abstract |
The purpose of the project was twofold : first, to determine the convergence behavior of the Fourier or Walsh Fourier series of so-called Zygmund class and second, to obtain integral inequalities which can be used in various scenes of mathmatical analysis.
The first problem turns out to be very difficult to attack, so our main effort centered around the second problem, intertwining with other branches of mathematical analysis, especially the theory of approximation of functions. Since very few results are reported on the approximation of functions belonging to the space BMO, the chief investigator tried to make up lecture notes on the topic, which will be appended in this report.
The Bernstein inequality is proved in this setting, then it is improved so as to yield easy treatment for applications. As a result, the whole theory is based on a few simple "tools", and this will show the extent of the vast extent of Bernstein's ideas.
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