collaborators

7 papers

math.CA2026

Loomis-Whitney inequalities on Reiter-Heisenberg groups

Sheng-Chen Mao, Ye Zhang

We establish a Loomis-Whitney inequality for the Reiter-Heisenberg groups , a family of step-two Carnot groups that includes the Heisenberg groups when . The…

math.CA2026

Dimension-free estimates for the full discrete Euclidean ball maximal function

Sheng-Chen Mao

Let denote the normalized average over the lattice points in the Euclidean ball of radius in . We prove that the full maximal operator $f\mapsto\sup_{t\geq0…

math.SP2026

Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds

Sheng-Chen Mao, Ye Zhang

Let \(N_M(λ)\) be the spectral counting function of the sub-Laplacian on the compact Heisenberg manifold \(M=Γ\backslash\mathbb H_d\), where is a lattice subgroup of the Heisen…

math.CA2026

A dichotomy for uniform Riesz transform bounds on stratified Lie groups

Sheng-Chen Mao, Yaojun Wang, Ye Zhang

Let be a stratified Lie group and be its sub-Laplacian. We prove that the full horizontal Riesz transform is of weak type $…

math.NT2026

Lattice point counting in Cygan--Korányi balls on Heisenberg groups

Sheng-Chen Mao, Sibei Yang

Lattice point counting in gauge balls on the Heisenberg group is a non-commutative analogue of the Euclidean multidimensional sphere problem, initiated by Garg, Nevo…

math.CA2026

Lattice point counting problems on step-two nilpotent Lie groups

Sheng-Chen Mao

We develop the theory of lattice point counting on connected and simply connected nilpotent Lie groups of step-two, endowed with the parabolic type dilation and a family of homogen…