Log-Sobolev inequalities and hypercontractivity for Ornstein-Uhlenbeck evolution operators in infinite dimensions
Authors: Davide A. Bignamini, Paolo De Fazio
Summary: In an infinite dimensional separable Hilbert area X, we research the realizations of Ornstein-Uhlenbeck evolution operators $pst$ within the areas $L^p(X,g_t)$, ${g_t}_{tinR}$ being the distinctive evolution system of measures for $pst$ in $R$. We show hyperconctractivity outcomes, counting on appropriate Log-Sobolev estimates. Among the many examples we contemplate the transition evolution operator of a non autonomous stochastic parabolic PDE.
