Relatively compact sets on abstract wiener space

Xi Cheng Zhang

doi:10.1007/s10114-005-0529-1

Relatively compact sets on abstract wiener space

Xi Cheng Zhang^*

^*此作品的通讯作者

Huazhong University of Science and Technology

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	819-822
页数	4
期刊	Acta Mathematica Sinica, English Series
卷	21
期	4
DOI	https://doi.org/10.1007/s10114-005-0529-1
出版状态	已出版 - 8月 2005
已对外发布	是

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Zhang, X. C. (2005). Relatively compact sets on abstract wiener space. Acta Mathematica Sinica, English Series, 21(4), 819-822. https://doi.org/10.1007/s10114-005-0529-1

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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.",

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N2 - 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.

AB - 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.

KW - Abstract Wiener space

KW - Mallinvin calculus

KW - Relatively compact sets

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Relatively compact sets on abstract wiener space

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