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- W2015455555 abstract "We obtain a martingale representation theorem for differentiable functions on loop space over a compact Riemannian manifold, which in turn yields a log-Sobolev inequality with a neat and explicit potential depending only on the curvature of the manifold and the Hessian of the heat kernel. Moreover, the potentiel term is Lp-integrable for all p ≥ 1. Nous obtenons dans cette Note un théorème de représentation de martingales pour les fonctions différentiables sur un espace de lacets au-dessus d'une variété de Riemann, qui entraîne une inégalité de Sobolev logarithmique avec un potentiel explicite dépendant seulement de la courbure de la variété et du hessien du noyau de la chaleur. Par ailleurs, le terme de potentiel est dans Lp pour tout p ≥ 1." @default.
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- W2015455555 date "1998-03-01" @default.
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- W2015455555 title "Martingale representation and log-Sobolev inequality on loop space" @default.
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- W2015455555 doi "https://doi.org/10.1016/s0764-4442(98)80043-8" @default.
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