Comptes Rendus
no. 6
Probability Theory
Relatively compact criteria for Hilbert valued random fields on abstract Wiener space
Presented by: Paul Malliavin
Xicheng Zhang1
1Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 437-440

In terms of the compact embedding theorems in finite dimensional Sobolev spaces, conditions are given under which Hilbert valued random fields on abstract Wiener space are relatively compact in some Lp-space.

Nous obtenons un nouveau critère pour qu'une famille de l'espace Lp(X,B), définie sur un espace de Wiener et à valeurs dans un espace de Banach B, soit compacte. La démonstration utilise l'approximation de dimension finie et l'hypercontractivité du semi-groupe d'Ornstein–Uhlenbeck. Notre résultat est différent d'un résultat récent de Bally–Saussereau dans le sens où nous travaillons dans Lp pour tout p>1 tandis que le résultat de Bally–Saussereau est limité à p=2.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.01.004

Xicheng Zhang  1

1 Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China 
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Xicheng Zhang. Relatively compact criteria for Hilbert valued random fields on abstract Wiener space. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 437-440. doi: 10.1016/j.crma.2006.01.004

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[5] A. Pazy Semi-Groups of Linear Operators and Applications, Springer-Verlag, Berlin, 1985

[6] X. Zhang Relatively compact sets on abstract Wiener space, Acta Math. Sinica, Volume 21 (2005) no. 4, pp. 819-822

[7] X. Zhang, Relatively compact families of functionals on abstract Wiener space and applications, J. Func. Anal., in press

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