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

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-09-13 DOI:10.1007/s00028-024-01005-1

Davide A. Bignamini, Paolo De Fazio

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.

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奥恩斯坦-乌伦贝克演化算子在无限维的对数-索博列夫不等式和超收缩性

在无穷维可分离的希尔伯特空间 X 中，我们研究 Ornstein-Uhlenbeck 演化算子 \(P_{s,t}\)在空间 \(L^p(X,\gamma _t)\)中的实现，\(\{gamma _t\}_{t\in \mathbb {R}}\)是 \(P_{s,t}\)的一个合适的度量演化系统。我们依靠合适的 Log-Sobolev 估计来证明超收缩性结果。在这些例子中，我们考虑了与非自治随机抛物线 PDE 相关的过渡演化算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

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