The L^p-Poincaré inequality for analytic Ornstein-Uhlenbeck operators

2014/02/13 by van Neerven, Jan
#35R60 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47D07 #Secondary: 35R15

paper · doi:10.48550/arxiv.1402.3185

Abstract

Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t≥ 0, where A generates a C₀-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure μ_∞ we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincaré inequality \n f - f\n_{L^p(E,μ_∞)} ≤ \n D_H f\n_{L^p(E,μ_∞)} holds for all 1

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