Poincaré inequality for weighted first order Sobolev spaces on loop spaces

DOI10.1006/jfan.2001.3775zbMath1011.60060OpenAlexW2084148084MaRDI QIDQ5952328

Michael Roeckner, Li-ming Wu, Fu-Zhou Gong

Publication date: 2 June 2003

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

Full work available at URL: https://doi.org/10.1006/jfan.2001.3775

zbMATH Keywords

Schrödinger operatorPoincaré inequalityspectral gapDirichlet formslog-Sobolev inequalityloop spacesOrnstein-Uhlenbeck operator

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Dirichlet forms (31C25) Markov semigroups and applications to diffusion processes (47D07) Schrödinger operator, Schrödinger equation (35J10) Diffusion processes and stochastic analysis on manifolds (58J65) Transition functions, generators and resolvents (60J35)

Related Items (12)

Absolute continuity of symmetric Markov processes. ⋮ Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDEs ⋮ EXPONENTIAL INTEGRABILITY FOR IMAGES OF ORNSTEIN–UHLENBECK OPERATORS ACTING ON CYLINDER FUNCTIONS ON LOOP SPACES ⋮ On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold ⋮ Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ On a certain semiclassical problem on Wiener spaces ⋮ Spectral gap of positive operators and applications ⋮ Weak Poincaré inequalities on domains defined by Brownian rough paths ⋮ A Poincaré inequality on loop spaces ⋮ Limit theorems for cloning algorithms ⋮ Spectral gaps of Schrödinger operators and diffusion operators on abstract Wiener spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities
• Logarithmic Sobolev inequalities on loop groups
• Analysis on Wiener spaces. II: Differential forms
• Integration on loop groups. II: Heat equation for the Wiener measure
• Dirichlet forms and analysis on Wiener space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• The log-Sobolev inequality on loop space over a compact Riemannian manifold
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• Differential calculus on path and loop spaces. II: Irreducibility of Dirichlet forms on loop spaces
• On the Ornstein-Uhlenbeck operators on Wiener-Riemannian manifolds
• Uniqueness of generalized Schrödinger operators. II
• Composite media and asymptotic Dirichlet forms
• Dirichlet forms and symmetric Markov processes
• Absolute continuity of symmetric diffusions
• Uniformly integrable operators and large deviations for Markov processes
• Exponential decay of positivity preserving semigroups on \(L^p\)
• Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups
• Positive generalized Wiener functions and potential theory over abstract Wiener spaces
• A function space large deviation principle for certain stochastic integrals
• Absolute continuity of heat kernel measure with pinned Wiener measure on loop groups
• Pinned Brownian motion and its perturbations
• Logarithmic Sobolev inequalities for pinned loop groups
• On the geometry of diffusion operators and stochastic flows
• Existence and uniqueness of invariant measures: An approach via sectorial forms
• Uniqueness of ground states for Schrödinger operators over loop groups
• Existence and uniqueness of physical ground states
• Girsanov-type transformations of local Dirichlet forms: An analytic approach
• Equivalence of heat kernel measure and pinned Wiener measure on loop groups
• A Remark on Nelson's Best Hypercontractive Estimates
• A Cameron-Martin Type Quasi-Invariance Theorem for Pinned Brownian Motion on a Compact Riemannian Manifold
• Spectral gap of positive operators and applications
• Markov Processes Associated With Positivity Preserving Coercive Forms
• Spectral gaps on loop spaces: a counterexample

This page was built for publication: Poincaré inequality for weighted first order Sobolev spaces on loop spaces