Gradient estimates for the heat semigroup on \(\mathbb H\)-type groups

DOI10.1007/s11118-010-9173-1zbMath1206.35241OpenAlexW2052396484MaRDI QIDQ711719

Hong-Quan Li, Jun-Qi Hu

Publication date: 27 October 2010

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-010-9173-1

zbMATH Keywords

heat semigroupgradient estimatesHeisenberg type groups

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) A priori estimates in context of PDEs (35B45) Analysis on other specific Lie groups (43A80) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (10)

Gradient estimates for Schrödinger operators with characterizations of 𝐵𝑀𝑂_{ℒ} on Heisenberg groups ⋮ Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups ⋮ Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups ⋮ Positive curvature property for sub-Laplacian on nilpotent Lie group of rank two ⋮ On the H.-Q. Li inequality on step-two Carnot groups ⋮ On complex H-type Lie algebras ⋮ Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups ⋮ Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups* ⋮ Gradient estimates for heat kernels and harmonic functions ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Cites Work

• Unnamed Item
• Unnamed Item
• Counter example to the Besicovitch covering property for some Carnot groups equipped with their Carnot-Carathéodory metric
• Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds
• Precise estimates for the subelliptic heat kernel on H-type groups
• On gradient bounds for the heat kernel on the Heisenberg group
• The subelliptic heat kernel on \(\mathbf{SU}(2)\): representations, asymptotics and gradient bounds
• Gradient estimates for the subelliptic heat kernel on H-type groups
• Nonlinear Liouville theorems for some critical problems on \(H\)-type groups.
• Estimations of the heat kernel on conic manifolds and applications
• Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the CCR heat flow
• Hypoelliptic heat kernel inequalities on the Heisenberg group
• Lower estimates of the heat kernel on conic manifolds and Riesz transform
• Analysis on geodesic balls of sub-elliptic operators
• About Riesz transforms on the Heisenberg groups
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• Riesz transform on manifolds and heat kernel regularity
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• Estimations optimales du noyau de la chaleur sur les groupes de type Heisenberg
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• An Optimal Representation Formula for Carnot-Carathéodory Vector Fields
• Characterisation of the sub-Riemannian isometry groups of theH-type groups
• The geometry of Markov diffusion generators

This page was built for publication: Gradient estimates for the heat semigroup on \(\mathbb H\)-type groups