We prove an optimal embedding result for the domains of Kolmogorov (or degenerate hypoelliptic Ornstein--Uhlenbeck) operators in L^2 spaces with respect to invariant measures. We use an interpolation method together with optimal L^2 estimates for the space derivatives of T(t)f near t=0, where T(t) is the Ornstein--Uhlenbeck semigroup and f is any function in L^2.
Invariant measures and maximal L^2 regularity for nonautonomous Ornstein-Uhlenbeck equations / Geissert, M; Lunardi, Alessandra. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 77:(2008), pp. 719-740. [10.1112/jlms/jdn009]
Invariant measures and maximal L^2 regularity for nonautonomous Ornstein-Uhlenbeck equations
LUNARDI, Alessandra
2008-01-01
Abstract
We prove an optimal embedding result for the domains of Kolmogorov (or degenerate hypoelliptic Ornstein--Uhlenbeck) operators in L^2 spaces with respect to invariant measures. We use an interpolation method together with optimal L^2 estimates for the space derivatives of T(t)f near t=0, where T(t) is the Ornstein--Uhlenbeck semigroup and f is any function in L^2.File in questo prodotto:
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