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, rely...

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Bibliographic Details
Published inarXiv.org
Main Authors Bignamini, Davide A, De Fazio, Paolo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.11.2023
Subjects
Evolution
Hilbert space
Operators
Parabolic differential equations
Partial differential equations
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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.
ISSN:2331-8422