Reverse hypercontractivity over manifolds
type: Item
instance of: scholarly article
title: Reverse hypercontractivity over manifolds
zbMATH Open document ID: 1021.58020
DOI: 10.1007/BF02384558
author: Fernando Galaz Fontes
author: Leonard Gross
author: Bruce Sontz
published in: Arkiv för Matematik
publication date: 2003-06-16T00:00:00Z
review text: Consider a vector field \(X\) over a manifold \(M\) whose flow \(\exp tX\) exists for any time. Let \(\mu\) be a measure on \(M\) for which the induced measures \(\mu_t\equiv(\exp tX)_*\mu\) are absolutely continuous with respect to \(\mu\). The authors establish bounds for the \(L^p(\mu)\) norm of the Radon-Nikodym derivative \(d\mu_t/d\mu\) in terms of the divergence of the field \(X\). In the case of a complex manifold \(M\) they derive reverse hypercontractivity bounds and reverse logarithmic Sobolev inequalities in some holomorphic function spaces. Examples are proposed on \({\mathbb C}^m\) and on the Riemann surface for \(z^{1/n}\).
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1928879
MaRDI profile type: Publication
cites work: Absolutely continuous flows generated by Sobolev class vector fields in finite and infinite dimensions
cites work: Some integral identities and inequalities for entire functions and their application to the coherent state transform
cites work: Flows associated to tangent processes on the Wiener space
cites work: Equations différentielles ordinaires: Non explosion et mesures quasi- invariantes
cites work: Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
cites work: Integration by parts and quasi-invariance for heat kernel measures on loop groups
cites work: Logarithmic Sobolev Inequalities
cites work: Hypercontractivity over complex manifolds
cites work: Strong hypercontractivity and relative subharmonicity
cites work: On hypercontractivity for multipliers on orthogonal polynomials
cites work: On complex hypercontractivity
cites work: A reverse log-Sobolev inequality in the Segal-Bargmann space
cites work: Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
cites work: The contractivity of the free Hamiltonian semigroup in the \(L^ p\) space of entire functions
description: scientific article; zbMATH DE number 1928879