| ALp -空间的单位球面上Lipschitz映射的等距延拓 |
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| 引用本文： | 高金梅,谭冬妮.ALp -空间的单位球面上Lipschitz映射的等距延拓[J].数学物理学报(A辑),2012,32(2):387-394. |
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| 作者姓名： | 高金梅 谭冬妮 |
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| 作者单位： | 1.青岛大学 数学科学学院 山东青岛 260071|
2.天津理工大学 数学系 天津 300071 |
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| 基金项目： | 教育部博士点基金(20060055010)和国家自然科学基金 (41171183)资助 |
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| 摘 要： | 该文研究了Lp(Ω,∑,μ; Lq(X, A,ν)) (2≤qp (Ω,∑,μ; Lq(X,A,ν))(1
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| 关 键 词： | 等距延拓 1-Lipschitz 映射 严格凸赋范空间 Bochner 积分 |
| 收稿时间： | 2010-11-25 |
| 修稿时间： | 2011-12-30 |
On Extension of Isometries Between Unit Spheres in ALp-spaces (1<p<∞) |
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| GAO Jin-Mei,TAN Dong-Ni.On Extension of Isometries Between Unit Spheres in ALp-spaces (1
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| Authors: | GAO Jin-Mei TAN Dong-Ni |
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| Institution: | 1.School of Mathematics, Qingdao University, Shandong Qingdao 266071;
2.School of Mathematics, Tianjin University of Technology, Tianjin 300071 |
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| Abstract: | In this paper, we discuss the 1-Lipschitz mappings between the unit spheres in vector valued spaces Lp(Ω, ∑, μ; Lq(X, A, ν)) (2≤q<p<∞) and anti-1-Lipschitz mappings between the unit spheres in vector valued spaces Lp (Ω, ∑, μ; Lq(X, A, ν))(1<p<≤2), and obtain that every such mapping can be extended to be a real linear isometry on the whole space Lp(Ω, ∑, μ; Lq(X, A, ν)). |
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