Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg

DOI10.1016/j.jfa.2006.02.016zbMath1106.22009OpenAlexW2058857173MaRDI QIDQ2497925

Hong-Quan Li

Publication date: 4 August 2006

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.02.016

zbMATH Keywords

Heisenberg groupheat kernelheat semigroupPoincaré inequality, representation formulasubriemannian structure

Mathematics Subject Classification ID

Heat equation (35K05) Analysis on real and complex Lie groups (22E30) Heat and other parabolic equation methods for PDEs on manifolds (58J35) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (54)

NOTES ON CONFORMAL PERTURBATION OF HEAT KERNELS ⋮ Coupling in the Heisenberg group and its applications to gradient estimates ⋮ Derivative formulas and Poincaré inequality for Kohn-Laplacian type semigroups ⋮ Estimations optimales du noyau de la chaleur sur les groupes de type Heisenberg ⋮ Estimates for invariant probability measures of degenerate SPDEs with singular and path-dependent drifts ⋮ Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups ⋮ Estimations Asymptotiques du Noyau de la Chaleur Pour L'opérateur de Grushin ⋮ Linear and nonlinear dissipative dynamics ⋮ Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group ⋮ The subelliptic heat kernel on the anti-de Sitter space ⋮ The subelliptic heat kernel on the CR sphere ⋮ Heat and entropy flows in Carnot groups ⋮ Gradient estimates for the heat kernels in higher dimensional Heisenberg groups ⋮ Positive curvature property for sub-Laplacian on nilpotent Lie group of rank two ⋮ Couplings in \(L^p\) distance of two Brownian motions and their Lévy area ⋮ Gradient bounds for Kolmogorov type diffusions ⋮ Asymptotic estimates for the heat kernel on Heisenberg groups ⋮ From \(U\)-bounds to isoperimetry with applications to H-type groups ⋮ On the H.-Q. Li inequality on step-two Carnot groups ⋮ Geometry and analysis of Dirichlet forms. II ⋮ Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ Coercive inequalities and U-bounds on step-two Carnot groups ⋮ Spectral inequalities for operators on \(H\)-type groups ⋮ \(q\)-Poincaré inequalities on Carnot groups with filiform type Lie algebra ⋮ On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group ⋮ Derivative formula and gradient estimates for Gruschin type semigroups ⋮ Precise estimates for the subelliptic heat kernel on H-type groups ⋮ Asymptotic estimates on the time derivative of \(\Phi\)-entropy on Riemannian manifolds ⋮ The subelliptic heat kernels on \(\mathbf{SL}(2,\mathbb{R})\) and on its universal covering \(\widetilde{\mathbf{SL}(2,\mathbb{R})}\): Integral representations and some functional inequalities ⋮ Dimension-free Harnack inequalities on \(\mathrm{RCD}(K, \infty )\) spaces ⋮ Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs ⋮ Coercive inequalities in higher-dimensional anisotropic Heisenberg group ⋮ Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups ⋮ Degenerate SDEs with singular drift and applications to Heisenberg groups ⋮ Hypoelliptic heat kernel inequalities on Lie groups ⋮ On gradient bounds for the heat kernel on the Heisenberg group ⋮ Hamilton type gradient estimate for the sub-elliptic operators ⋮ Positive curvature property for some hypoelliptic heat kernels ⋮ Duality on gradient estimates and Wasserstein controls ⋮ Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups* ⋮ Analysis on extended Heisenberg group ⋮ Ornstein-Uhlenbeck semi-groups on stratified groups ⋮ Gradient estimates for the heat semigroup on \(\mathbb H\)-type groups ⋮ Ergodicity of Markov semigroups with Hörmander type generators in infinite dimensions ⋮ Diffusion by optimal transport in Heisenberg groups ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ Log-Harnack inequality for Gruschin type semigroups ⋮ Stochastic completeness and gradient representations for Sub-Riemannian manifolds ⋮ The subelliptic heat kernel on \(\mathbf{SU}(2)\): representations, asymptotics and gradient bounds ⋮ Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality ⋮ Gradient estimates for the subelliptic heat kernel on H-type groups ⋮ Coercive inequalities on metric measure spaces ⋮ A convergence to Brownian motion on sub-Riemannian manifolds ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

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• An Optimal Representation Formula for Carnot-Carathéodory Vector Fields
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