arXiv subjects

Shuai Qi

Publications and source records attributed to Shuai Qi.

3 recordsLinked to original sources

arXiv2025

Optimal asymptotic expansion of entire solutions to Monge-Ampère equation with $C^α$ perturbed periodic data

We consider the asymptotic behavior at infinity of solution $u$ to Monge-Ampère equation $\det(D^2u)=f$ in $\rn$, where $f$ is a perturbation of a periodic function and is only assumed to be Hölder continuous, compared to the previous work that $f$ is at least $C^{1,\az}$. The consequence established in this paper, by a nonlocal method, is that the difference between $u$ and a quadratic polynomial is asymptotically close to a periodic function.

math.AP↗

arXiv2025

Asymptotic expansion at infinity of solutions to Monge-Ampère equation with $C^α$ right term

We develop a non-local method to establish the asymptotic expansion at infinity of solutions to Monge-Ampère equation $\det(D^2v)=f$ on $\rn$, where $f$ is a perturbation of $1$ and is only assumed to be Hölder continuous outside a bounded subset of $\rn$, compared to the previous work that $f$ is at least $C^2$.

math.AP↗

arXiv2023

Endpoint theory for the compactness of commutators

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of commutators at the endpoint. The paper provides a comprehensive study of the compactness properties of commutators of Calderón-Zygmund operators in Hardy and $L^{1}(\mathbb{R}^n)$ type spaces. Additionally, we provide factorization theorems for Hardy spaces in terms of singular integral operators in the $L^1(\mathbb{R}^n)$ space.

math.FA↗