{"title":"Log-Sobolev inequalities and hypercontractivity for Ornstein – Uhlenbeck evolution operators in infinite dimension","authors":"Davide A. Bignamini, Paolo De Fazio","doi":"10.1007/s00028-024-01005-1","DOIUrl":null,"url":null,"abstract":"<p>In an infinite-dimensional separable Hilbert space <i>X</i>, we study the realizations of Ornstein–Uhlenbeck evolution operators <span>\\(P_{s,t}\\)</span> in the spaces <span>\\(L^p(X,\\gamma _t)\\)</span>, <span>\\(\\{\\gamma _t\\}_{t\\in \\mathbb {R}}\\)</span> being a suitable evolution system of measures for <span>\\(P_{s,t}\\)</span>. We prove hypercontractivity results, relying on suitable Log-Sobolev estimates. Among the examples, we consider the transition evolution operator associated with a non-autonomous stochastic parabolic PDE.\n</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"213 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Evolution Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00028-024-01005-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In an infinite-dimensional separable Hilbert space X, we study the realizations of Ornstein–Uhlenbeck evolution operators \(P_{s,t}\) in the spaces \(L^p(X,\gamma _t)\), \(\{\gamma _t\}_{t\in \mathbb {R}}\) being a suitable evolution system of measures for \(P_{s,t}\). We prove hypercontractivity results, relying on suitable Log-Sobolev estimates. Among the examples, we consider the transition evolution operator associated with a non-autonomous stochastic parabolic PDE.
期刊介绍：
The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications.
Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field.
Particular topics covered by the journal are:
Linear and Nonlinear Semigroups
Parabolic and Hyperbolic Partial Differential Equations
Reaction Diffusion Equations
Deterministic and Stochastic Control Systems
Transport and Population Equations
Volterra Equations
Delay Equations
Stochastic Processes and Dirichlet Forms
Maximal Regularity and Functional Calculi
Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations
Evolution Equations in Mathematical Physics
Elliptic Operators
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