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Sheng-Chen Mao

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Preprint Sep 2026

Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds

Let $N_M(\lambda)$ be the spectral counting function of the sub-Laplacian on the compact Heisenberg manifold $M=\Gamma\backslash\mathbb H_d$, where $\Gamma$ is a lattice subgroup of the Heisenberg group $\mathbb H_d$. In 2016, Strichartz \cite[\textit{J. Geom. Anal.}]{Str16} proved the Weyl law with remainder \(R_M...

Sheng-Chen Mao, Ye Zhang · 0 citations

Preprint Aug 2026

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

Let $\mathbb{G}$ be a stratified Lie group and $\mathcal L$ be its sub-Laplacian. We prove that the full horizontal Riesz transform $\nabla_{H} \mathcal L^{-1/2}$ is of weak type $(1,1)$ on real-valued functions, with constant at most $2$. In particular, the constant is independent of the horizontal dimension, the homo...

Sheng-Chen Mao, Yaojun Wang, Ye Zhang · 1 citation

Preprint Sep 2026

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

Let $M_t$ denote the normalized average over the lattice points in the Euclidean ball of radius $t$ in $\mathbb{Z}^d$. We prove that the full maximal operator $f\mapsto\sup_{t\geq0}\lvert M_t f\rvert$ is bounded on $\ell^p(\mathbb{Z}^d)$, for every $1<p\leq\infty$, with a constant independent of the dimension. In parti...

Sheng-Chen Mao · 0 citations