| DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES |
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| 作者姓名： | 宋迎清 杨孝平 刘振海 |
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| 作者单位： | School of Science，Nanjing University of Science and Technology，Nanjing 210094，China Department of Mathematics，Hunan University of City，Yiyang 413000，China，School of Science，Nanjing University of Science and Technology，Nanjing 210094，China，Department of Mathematics，Changsha University of Electrical Power，Changsha 410077，China |
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| 基金项目： | NNSF of China (19771048) |
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| 摘 要： | The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the
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DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATH(E)ODORY SPACES |
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| Song Yingqing Yang Xiaoping Liu Zhenghai
.School of Science,Nanjing University of Science and Technology,Nanjing ,China.DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES[J].Acta Mathematica Scientia,2003,23(4). |
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| Authors: | Song Yingqing Yang Xiaoping Liu Zhenghai
School of Science Nanjing University of Science and Technology Nanjing China |
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| Institution: | Song Yingqing Yang Xiaoping Liu Zhenghai
1.School of Science,Nanjing University of Science and Technology,Nanjing 210094,China
2.Department of Mathematics,Hunan University of City,Yiyang 413000,China 3.Department of Mathematics,Changsha University of Electrical Power,Changsha 410077,China |
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| Abstract: | The aim of this paper is to get the decomposition of distributional derivativesof functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose theapproximate continuity of BV functions is discussed first, then approximate differentialsof L1 functions are defined in the case that vector fields are of Carnot type and finally thedecomposition Xu = △u @ Ln + Xsu is proved, where u ∈ BVx(Ω) and △u denotes theapproximate differential of u. |
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| Keywords: | BV function C-C space Radon measure vector field approximate differential |
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