Sheng-Chen Mao

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20232026

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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 $G_{q p}$ , a family of step-two Carnot groups that includes the Heisenberg groups when $q = 1$ . The…

math.CA2026

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

Sheng-Chen Mao

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

math.CA2026

A $p = 2$ dichotomy for uniform Riesz transform bounds on stratified Lie groups

Sheng-Chen Mao, Yaojun Wang, Ye Zhang

Let $G$ be a stratified Lie group and $L$ be its sub-Laplacian. We prove that the full horizontal Riesz transform $\nabla_{H} L^{- 1/2}$ is of weak type $…

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…

Loomis-Whitney inequalities on Reiter-Heisenberg groups

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

A p=2 dichotomy for uniform Riesz transform bounds on stratified Lie groups

Lattice point counting problems on step-two nilpotent Lie groups

A $p = 2$ dichotomy for uniform Riesz transform bounds on stratified Lie groups