Harmonic analysis in a domain with fractal boundary
| Project/Area Number |
14540157
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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 | Ochanomizu University |
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Principal Investigator |
WATANABE Hisako Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (70017193)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEO Fukiko Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (40109228)
YOSHIDA Hidenobu Chiba Univ., Graduate School of Natural Sciences, Professor, 大学院・自然科学研究科, 教授 (60009280)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | fractal lateral boundary / double layer heat potentials / Whitney decomposition / Besov spaces / Besov norms / maximal functions / uniform domains / boundedness of operators / 擬距離空間 / donbling測度 / 極大関数 / 容量による積分 / weak type評価 / ベゾフ空間 / 放物型シリンダー / ホモジニアス型空間 / α-Rieszポテンシャル / ダブリング測度 / ベゾフノルム / 放物型Whitny分解 / 作用素の有界性 / 特異積分 / フラクタルな側面 |
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| Research Abstract |
We consider the initial-boundary-value problems in a domain Ω=D×[O,T] with fractal lateral boundary S. It often occurs that an operator K on the Besov space B on the lateral boundary is bounded with respect to the Besov norms on S. We can prove the boundedness of an operator from B to B in the following method.
(1)We extend a function f defined on S to R×[O,T] by using an extension operator E.
(2)The Besov norm of f is estimated by the integral of |▽f(x)|×δ(x)^n over Ω, where δ(x) is the distance from x to S and n is a suitable number.
(3)Instead of the boundedness of K we prove the boundedness of an operator from a function space on Ω to a function space on the outside of Ω by using the maximal functions between Ω and the outside of Ω.
We proved the boundedness of an operator K, which is important to solve the Dirichlet problem by using double layer heat potentials.
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Report
(4 results)
Research Products
(16 results)
