6 citations · 16 across the 12 of their papers we have counts for
13 papers
The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds
Rui Chen, Renjin Jiang, Bo Li +1
Let be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type , with constant for real-valued functions. Consequently, it is…
Uniform heat kernel asymptotics for the Grushin operator
Yimeng Chen, Hong-Quan Li, Jun-Cheng Tang +1
Adopting the powerful methods introduced in \cite{li2021carnotcaratheodory, LZ2025}, we investigate the asymptotic behaviour at infinity for the heat kernel associated with the Gru…
Uniform volume estimates and maximal functions on generalized Heisenberg-type groups
Cheng Bi, Hong-Quan Li
On generalized Heisenberg-type groups , we give uniform volume estimates for the ball defined by a large class of Carnot-Carathéodory distan…
Weak type of Riesz transform on some direct product manifolds with exponential volume growth
Hong-Quan Li, Jie-Xiang Zhu
In this paper we are concerned with the Riesz transform on the direct product manifold , where is the -dimensional real hyperbolic spac…
Riesz transform on manifolds with ends of different volume growth for
Renjin Jiang, Hongquan Li, Haibo Lin
Let , , be complete, connected and non-collapsed manifolds of the same dimension, where , and suppose that each satisfies a doub…
A complete answer to the Gaveau--Brockett problem
Hong-Quan Li, Ye Zhang
The note is dedicated to provide a satisfying and complete answer to the long-standing Gaveau--Brockett open problem. More precisely, we determine the exact formula of the Carnot--…
The Carnot-Carathéodory distance on -step groups
Hong-Quan Li
Combining Varadhan's formula, Loewner's theorem with the method of stationary phase, we study the exact formula of the Carnot-Carathéodory distance on -step groups. The method i…
Sub-Riemannian geometry on some step-two Carnot groups
Hong-Quan Li, Ye Zhang
This paper is a continuation of the previous work of the first author. We characterize a class of step-two groups introduced in \cite{Li19}, saying GM-groups, via some basic sub-Ri…
Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups
Hong-Quan Li, Ye Zhang
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…
Lower bound of Riesz transform kernels revisited and commutators on stratified Lie groups
Xuan Thinh Duong, Hong-Quan Li, Ji Li +2
Let be a stratified Lie group and $\{\X_j\}_{1 \leq j \leq n}$ a basis for the left-invariant vector fields of degree one on . Let $Δ= \sum_{j = 1}^n \X_j^…
Lower bound of Riesz transform kernels and Commutator Theorems on stratified nilpotent Lie groups
Xuan Thinh Duong, Hong-Quan Li, Ji Li +1
We provide a study of the Riesz transforms on stratified nilpotent Lie groups, and obtain a certain version of the pointwise lower bound of the Riesz transform kernel. Then we esta…
Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space
Hong-Quan Li, Peter Sjögren
Let be a vector in . Consider the Laplacian on with drift and the measure , with respect t…
Centered Hardy-Littlewood maximal function on hyperbolic spaces,
Hong-Quan Li
In this paper, we prove () dimension free bounds for the centered Hardy-Littlewood maximal function on real or complex hyperbolic spaces.