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^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	819-822
Number of pages	4
Journal	Acta Mathematica Sinica, English Series
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s10114-005-0529-1
Publication status	Published - Aug 2005
Externally published	Yes

Keywords

Abstract Wiener space
Mallinvin calculus
Relatively compact sets

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10.1007/s10114-005-0529-1

Cite this

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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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JO - Acta Mathematica Sinica, English Series

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Relatively compact sets on abstract wiener space

Abstract

Keywords

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