| Relatively Compact Sets on Abstract Wiener Space |
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| 引用本文： | Xi Cheng ZHANG. Relatively Compact Sets on Abstract Wiener Space[J]. 数学学报(英文版), 2005, 21(4): 819-822. DOI: 10.1007/s10114-005-0529-1 |
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| 作者姓名： | Xi Cheng ZHANG |
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| 作者单位： | Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China |
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| 基金项目： | This work is supported by NSF （No.10301011） of China and Project 973. |
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| 摘 要： | In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.
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| 关 键 词： | 紧集 Wiener空间 Malliavin微积分学 Prato-Malliavin空间 |
| 收稿时间： | 2003-04-01 |
| 修稿时间： | 2003-04-012003-08-26 |
Relatively Compact Sets on Abstract Wiener Space |
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| Xi Cheng Zhang. Relatively Compact Sets on Abstract Wiener Space[J]. Acta Mathematica Sinica(English Series), 2005, 21(4): 819-822. DOI: 10.1007/s10114-005-0529-1 |
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| Authors: | Xi Cheng Zhang |
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| Affiliation: | (1) Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China |
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| Abstract: | In this note, we obtain a sufficient and necessary condition for a set in an abstract Wiener space (X, H, μ) to be relatively compact in L 2(X, μ). Meanwhile, we give a sufficient condition for relative compactness in L p (X, μ) for p > 1. We also provide an example of Da Prato–Malliavin–Nualart to show the result. This work is supported by NSF (No. 10301011) of China and Project 973 |
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| Keywords: | Relatively compact sets Abstract Wiener space Malliavin calculus |
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