| Some Applications of Besov Spaces on Fractals |
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| 作者姓名： | Da Chun YANG |
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| 作者单位： | Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| 基金项目： | The author is partially supported by NNSF （10271015） and RFDP （20020027004） of China |
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| 摘 要： | Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ） of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0（F） and Fpq^0（F）.
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| 关 键 词： | Besov空间 Sobolev空间 嵌入理论 伪微分算子 椭圆算子 |
| 收稿时间： | 2002-10-20 |
| 修稿时间： | 2002-10-202003-01-14 |
Some Applications of Besov Spaces on Fractals |
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| Da Chun YANG.Some Applications of Besov Spaces on Fractals[J].Acta Mathematica Sinica,2005,21(5):1209-1218. |
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| Authors: | Da Chun Yang |
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| Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | Let Γ be a compact d–set in ℝn with 0 < d ≤ n, which includes various kinds of fractals.
The author establishes an embedding theorem for the Besov spaces
$
B^{s}_{{pq}} (\Gamma )
$
B^{s}_{{pq}} (\Gamma )
of Triebel and the Sobolev
spaces W
1,p(Γ, d, μ) of Hajłasz when s > 1, 1 < p < ∞ and 0 < q ≤ ∞. The author also gives some
applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal
pseudodifferential operators in the spaces
$
B^{0}_{{pq}} (\Gamma )
$
B^{0}_{{pq}} (\Gamma )
and
$
F^{0}_{{pq}} (\Gamma ).
$
F^{0}_{{pq}} (\Gamma ). |
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| Keywords: | Besov spaces Fractals Sobolev spaces Pseudodifferential operators Elliptic operators Eigenvalues |
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