A unification of hypercontractivities of the Ornstein-Uhlenbeck semigroup and its connection with {\(\Phi\)}-entropy inequalities

DOI10.1016/j.jfa.2018.08.009OpenAlexW2888158173MaRDI QIDQ1785770

Yuu Hariya

Publication date: 1 October 2018

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2018.08.009

zbMATH Keywords

logarithmic Sobolev inequalityhypercontractivityOrnstein-Uhlenbeck semigroup\(\Phi\)-entropy

Mathematics Subject Classification ID

Brownian motion (60J65) Markov semigroups and applications to diffusion processes (47D07) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items (2)

A modified \(\Phi \)-Sobolev inequality for canonical Lévy processes and its applications ⋮ The Boué-Dupuis formula and the exponential hypercontractivity in the Gaussian space

Cites Work

• Modified logarithmic Sobolev inequalities in discrete settings
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• The free Markoff field
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• The Malliavin Calculus and Related Topics
• Logarithmic Sobolev Inequalities
• Isoperimetric Functional Inequalities via the Maximum Principle: The Exterior Differential Systems Approach
• Analysis and Geometry of Markov Diffusion Operators
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