| FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS |
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| 引用本文： | DENG Donggao,XU Ming,YAN Lixin. FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS[J]. 数学年刊B辑(英文版), 2005, 26(2): 229-238 |
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| 作者姓名： | DENG Donggao XU Ming YAN Lixin |
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| 作者单位： | DENG Donggao XU Ming YAN Lixin Department of Mathematics，Zhongshan University，Guangzhou 510275，China. Institute of Mathematics，Chinese Academy of Sciences，Beijing 100080，China. Department of Mathematics，Zhongshan University，Guangzhou 510275，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10171111, No.10371734)and the Foundation of Advanced Research Center, Zhongshan University. |
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| 摘 要： | §1. IntroductionLet L be a homogeneous elliptic operator on L2(Rn) of order 2m in divergence formL = (?1)m|α|=|β|=m?α(aα,β?β), (1.1)where we assume aα,β ∈ L∞(Rn;C) for all α,β. The operator L is associated to the followingform Q(f,g) de?ned o
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| 关 键 词： | 正则函数积分 高阶椭圆型算子 Hardy-Littlewood-Sobolev定理 复插值 |
| 收稿时间： | 2008-01-04 |
FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS |
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| DENG Donggao,XU Ming and YAN Lixin. FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS[J]. Chinese Annals of Mathematics,Series B, 2005, 26(2): 229-238 |
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| Authors: | DENG Donggao XU Ming YAN Lixin |
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| Affiliation: | 1. Department of Mathematics,Zhongshan University,Guangzhou 510275,China
2. Institute of Mathematics,Chinese Academy of Sciences,Beijing 100080,China |
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| Abstract: | The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L-α/2 for 0 ＜α＜ n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn. |
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| Keywords: | Fractional integrals Higher order elliptic operator Hardy-Littlewood- Sobolev theorem |
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