Log-Sobolev inequalities and hypercontractivity for Ornstein-Uhlenbeck evolution operators in infinite dimensions

In an infinite dimensional separable Hilbert space $X$, we study the realizations of Ornstein-Uhlenbeck evolution operators $\pst$ in the spaces $L^p(X,\g_t)$, $\{\g_t\}_{t\in\R}$ being the unique evolution system of measures for $\pst$ in $\R$. We prove hyperconctractivity results, relying on suita...

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Bibliographic Details
Main Authors Bignamini, Davide A, De Fazio, Paolo
Format Journal Article
LanguageEnglish
Published 13.09.2023
Subjects
Mathematics - Analysis of PDEs
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Summary:In an infinite dimensional separable Hilbert space $X$, we study the realizations of Ornstein-Uhlenbeck evolution operators $\pst$ in the spaces $L^p(X,\g_t)$, $\{\g_t\}_{t\in\R}$ being the unique evolution system of measures for $\pst$ in $\R$. We prove hyperconctractivity results, relying on suitable Log-Sobolev estimates. Among the examples we consider the transition evolution operator of a non autonomous stochastic parabolic PDE.
DOI:10.48550/arxiv.2309.07319