Author

Li-Xin Yan

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Preprint Sep 2026

Inequalities for radial solutions to the wave equation on the hyperbolic space

Let $\mathbb H^n$ be the $n$-dimensional hyperbolic space, and $\Delta_{\mathbb H^n}$ be the Laplace--Beltrami operator on $\mathbb H^n$. Let $u=u(t,\cdot)$ be the solution to the wave equation $\partial^2_{t}u-\big(\Delta_{\mathbb H^n}+\frac{1}{4}(n-1)^2\operatorname{Id}\big)u=0$ with initial conditions $u(0,x)=f(x)$...

Peng Chen, X. Duong, Yun-Xiang Wang et al. · 0 citations

Preprint Sep 2026

The weak-type $(1,1)$ estimates for wave equation on $ax+b$ groups

Let $G$ be the group $\mathbb{R}_+\ltimes \mathbb{R}^n$ endowed with Riemannian symmetric space metric $d$ and the right Haar measure $\mathrm{d} \rho$ which is of $ax+b$ type, and $L$ be the positive definite distinguished left-invariant Laplacian on $G$. Let $u=u(t,\cdot)$ be the solution to $u_{tt}+Lu=0$ with initia...

Yun-Xiang Wang, Li-Xin Yan · 0 citations

Preprint Sep 2026

Fefferman--Stein type inequalities via area and maximal functions for Schr\"odinger operators with applications

In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schr\"odinger operator $\mathcal{L} = -\Delta + V$ on stratified Lie groups $\mathcal G$, where $\Delta$ denotes the sub-Laplacian on $\mathcal G$ and $V$ is a nonnegative locally...

Ji Li, Wan Li, Liang Song et al. · 0 citations