Dimension dependent hypercontractivity for Gaussian kernels

DOI10.1007/s00440-011-0387-yzbMath1408.60068arXiv1003.5072OpenAlexW2079034004MaRDI QIDQ1934356

Ivan Gentil, François Bolley, Dominique Bakry

Publication date: 28 January 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5072

zbMATH Keywords

logarithmic Sobolev inequalitydiffusion semigroupcurvature-dimension criteriontransportation inequalityhypercontractive bound

Mathematics Subject Classification ID

Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65) Transition functions, generators and resolvents (60J35)

Related Items (13)

The Poisson equation and estimates for distances between stationary distributions of diffusions ⋮ On extension and refinement of the Poincaré inequality ⋮ Intrinsic dimensional functional inequalities on model spaces ⋮ A supersolutions perspective on hypercontractivity ⋮ Weighted Nash inequalities ⋮ The Weyl calculus with respect to the Gaussian measure and restricted Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time ⋮ Bounds on the deficit in the logarithmic Sobolev inequality ⋮ \(H^{\infty}\)-calculus for semigroup generators on BMO ⋮ Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities ⋮ Dimension-independent estimates for heat operators and harmonic functions ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ – OFF-DIAGONAL ESTIMATES FOR THE ORNSTEIN–UHLENBECK SEMIGROUP: SOME POSITIVE AND NEGATIVE RESULTS ⋮ On the \(L^\infty \)-uniqueness of symmetric diffusion operators on complete non-compact Riemannian manifolds

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