# Precise estimates for the subelliptic heat kernel on H-type groups

@article{Eldredge2009PreciseEF, title={Precise estimates for the subelliptic heat kernel on H-type groups}, author={Nathaniel Eldredge}, journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, year={2009}, volume={92}, pages={52-85} }

## 44 Citations

Hypoelliptic heat kernel inequalities on H-type groups

- Mathematics
- 2009

We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function…

The Subelliptic Heat Kernel on the Anti-de Sitter Space

- Mathematics
- 2012

We study the subelliptic heat kernel of the sub-Laplacian on a 2n+1-dimensional anti-de Sitter space ℍ2n+1 which also appears as a model space of a CR Sasakian manifold with constant negative…

Short-time asymptotics of heat kernels of hypoelliptic Laplacians on unimodular Lie groups

- Mathematics
- 2012

Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups*

- MathematicsCommunications in Partial Differential Equations
- 2019

Abstract The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three-dimensional case. Second,…

A note on gradient estimates for the heat semigroup on nonisotropic Heisenberg groups

- Mathematics
- 2021

Abstract. In this note we obtain gradient estimates for the heat semigroup on nonisotropic Heisenberg groups. More precisely, our aim is to get the H.-Q. Li inequality on nonisotropic Heisenberg…

Functional inequalities for subelliptic heat kernels

- Mathematics
- 2009

In this thesis, I have studied the heat kernel, the heat semigroup and the associated functional inequalities on three model spaces in subelliptic geometry. The main interest of this study is in fact…

Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups

- Mathematics
- 2017

Gradient Estimates for the Heat Semigroup on H-Type Groups

- Mathematics
- 2010

AbstractBy utilizing the Poincaré inequality and representation formulae, it is shown that on the Heisenberg type group, ℍ(2n, m), there exists a constant C > 0 such that
$$ |\nabla e^{t \Delta}…

A HARDY INEQUALITY ON H-TYPE GROUPS

- Mathematics
- 2012

Abstract. We prove a Hardy inequality related to Carnot-Carath´eodorydistance on H-type groups based on a representation formula on suchgroups. 1. IntroductionThe Hardy inequality in R N states that,…

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