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Under the assumption that the solutions to this equation admit an invariant measure \\mu_\\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\\'e inequality \\n f - \\overline f\\n_{L^p(E,\\mu_\\infty)} \\le \\n D_H f\\n_{L^p(E,\\mu_\\infty)} holds for all 1<p<\\infty. 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