Ziming Shi

activity

20192024

most citedNew Estimates of Rychkov's Universal Extension Operator for Lipschitz Domains and Some Applications

8 citations · 10 across the 8 of their papers we have counts for

collaborators

9 papers

math.CV2024

Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds

Xianghong Gong, Ziming Shi

Let $M$ be a relatively compact $C^{2}$ domain in a complex manifold $M$ of dimension $n$ . Assume that $H^{1} (M, Θ) = 0$ where $Θ$ is the sheaf of germs of holomorphic tangent…

math.AP2024

A unique continuation property for $∣ \partial u ∣ \leq V ∣ u ∣$

Ziming Shi

Let $u : Ω \subset C^{n} \to C^{m}$ , for $n \geq 2$ and $m \geq 1$ . Let $1 \leq p \leq 2$ , and $2 (2 n)^{2} - 1 \leq q < \infty$ such that $\displaystyle \frac{1}{p} + \frac{1…

math.CV2023

On $1/2$ estimate for global Newlander-Nirenberg theorem

Ziming Shi

Given a formally integrable almost complex structure $X$ defined on the closure of a bounded domain $D \subset C^{n}$ , and provided that $X$ is sufficiently close to the stan…

math.CV2022

Boundary Regularity of Bergman Kernel in Hölder space

Ziming Shi

Let $D$ be a bounded strictly pseudoconvex domain in $C^{n}$ . Assuming $b D \in C^{k + 3 + α}$ where $k$ is a non-negative integer and $0 < α \leq 1$ , we show that 1) the Bergman…

math.CA2022

Sobolev Differentiability Properties of Logarithmic Modulus of Real Analytic Functions

Ziming Shi, Ruixiang Zhang

Let $f$ be the germ of a real analytic function at the origin in $R^{n}$ for $n \geq 2$ , and suppose the codimension of the zero set of $f$ at $0$ is at least $2$ .…

math.CV2021

A Solution Operator for the $\partial$ Equation in Sobolev Spaces of Negative Index

Ziming Shi, Liding Yao

Let $Ω$ be a strictly pseudoconvex domain in $C^{n}$ with $C^{k + 2}$ boundary, $k \geq 1$ . We construct a $\partial$ solution operator (depending on $k$ ) that gains…

math.CA2021★ 8 cited

New Estimates of Rychkov's Universal Extension Operator for Lipschitz Domains and Some Applications

Ziming Shi, Liding Yao

Given a bounded Lipschitz domain $Ω \subset R^{n}$ , Rychkov showed that there is a linear extension operator $E$ for $Ω$ which is bounded in Besov and Triebel-Lizorkin…

math.CV2021★ 2 cited

Sobolev $\frac{1}{2}$ estimates for $\partial$ equations on strictly pseudoconvex domains with $C^{2}$ boundary

Ziming Shi, Liding Yao

We construct a solution operator for $\partial$ equation that gains $\frac{1}{2}$ derivative in the fractional Sobolev space $H^{s, p}$ on bounded strictly pseudoconvex d…

math.CV2019

Weighted Sobolev $L^{p}$ estimates for homotopy operators on strictly pseudoconvex domains with $C^{2}$ boundary

Ziming Shi

We derive estimates in a weighted Sobolev space $W_{μ}^{k, p} (D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^{2}$ boundary in ${\C}^n$. As a result, we…

Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds

A unique continuation property for ∣∂u∣≤V∣u∣

On 1/2 estimate for global Newlander-Nirenberg theorem

Boundary Regularity of Bergman Kernel in Hölder space

Sobolev Differentiability Properties of Logarithmic Modulus of Real Analytic Functions

A Solution Operator for the ∂ Equation in Sobolev Spaces of Negative Index

New Estimates of Rychkov's Universal Extension Operator for Lipschitz Domains and Some Applications

Sobolev 21​ estimates for ∂ equations on strictly pseudoconvex domains with C2 boundary

Weighted Sobolev Lp estimates for homotopy operators on strictly pseudoconvex domains with C2 boundary

A unique continuation property for $∣ \partial u ∣ \leq V ∣ u ∣$

On $1/2$ estimate for global Newlander-Nirenberg theorem

A Solution Operator for the $\partial$ Equation in Sobolev Spaces of Negative Index

Sobolev $\frac{1}{2}$ estimates for $\partial$ equations on strictly pseudoconvex domains with $C^{2}$ boundary

Weighted Sobolev $L^{p}$ estimates for homotopy operators on strictly pseudoconvex domains with $C^{2}$ boundary