Liding Yao

activity

20202025

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

8 citations · 23 across the 14 of their papers we have counts for

collaborators

14 papers

math.CV2025

On $\partial$ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates

Liding Yao, Yuan Zhang

We construct homotopy formulae $f = \partial H_{q} f + H_{q + 1} \partial f$ for $(0, q)$ forms on the product domain $Ω_{1} \times \dots \times Ω_{m}$ , where each…

math.CV2024

A universal $\partial$ solution operator on nonsmooth strongly pseudoconvex domains

Liding Yao

We construct a universal family of $\partial$ homotopy operators on bounded $C^{1, 1}$ domains that are locally strongly $C$ -linearly convexifiable. In particular t…

math.FA2024

A linear operator bounded in all Besov but not in Triebel-Lizorkin spaces

Liding Yao

We construct a linear operator $T : S^{'} (R^{n}) \to S^{'} (R^{n})$ such that $T : B_{pq}^{s} (R^{n}) \to B_{pq}^{s} (R^{n})$ for all $0<p,q…

math.CA2022★ 3 cited

On Seeley-type Universal Extension Operators for the Upper Half Space

Haowen Lu, Liding Yao

Modified from the standard half-space extension via reflection principle, we construct a linear extension operator for the upper half space $R_{+}^{n}$ that has the form $Ef(x)=\s…

math.CA2022

On Rough Frobenius-type Theorems and Their Hölder Estimates

Liding Yao

The thesis studies Frobenius-type theorems in non-smooth settings. We extend the definition of involutivity to non-Lipschitz subbundles using generalized functions. We prove the re…

math.CV2022★ 2 cited

Sobolev and Hölder estimates for homotopy operators of the $\partial$ -equation on convex domains of finite multitype

Liding Yao

We construct homotopy formulas for the $\partial$ -equation on convex domains of finite type that have optimal Sobolev and Hölder estimates. For a bounded smooth finite typ…

math.CV2022

Sharp Hölder Regularity for Nirenberg's Complex Frobenius Theorem

Liding Yao

Nirenberg's famous complex Frobenius theorem gives necessary and sufficient conditions on a locally integrable structure for when the manifold is locally diffeomorphic to $\mathbb…

math.FA2021★ 6 cited

Some Intrinsic Characterizations of Besov-Triebel-Lizorkin-Morrey-type Spaces on Lipschitz Domains

Liding Yao

We give Littlewood-Paley type characterizations for Besov-Triebel-Lizorkin-type spaces $B_{pq}^{s τ}, F_{pq}^{s τ}$ and Besov-Morrey spaces $N_{u q p}^{s}$ on a…

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.CA2021★ 1 cited

Improving the Regularity of Vector Fields

Brian Street, Liding Yao

Let $α > 0$ , $β > α$ , and let $X_{1}, \dots, X_{q}$ be $C_{loc}^{α}$ vector fields on a $C^{α + 1}$ manifold which span the tangent space at every point, where $\m…

math.CA2020

The Frobenius Theorem for Log-Lipschitz Subbundles

Liding Yao

We extend the definition of involutivity to non-Lipschitz tangent subbundles using generalized functions. We prove the Frobenius Theorem with sharp regularity estimate when the sub…

math.CV2020★ 1 cited

A Counterexample to $C^{k}$ -regularity for the Newlander-Nirenberg Theorem

Liding Yao

We give an example of $C^{k}$ -integrable almost complex structure that does not admit a corresponding $C^{k + 1}$ -complex coordinate system.

On ∂ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates

A universal ∂ solution operator on nonsmooth strongly pseudoconvex domains

A linear operator bounded in all Besov but not in Triebel-Lizorkin spaces

On Seeley-type Universal Extension Operators for the Upper Half Space

On Rough Frobenius-type Theorems and Their Hölder Estimates

Sobolev and Hölder estimates for homotopy operators of the ∂-equation on convex domains of finite multitype

Sharp Hölder Regularity for Nirenberg's Complex Frobenius Theorem

Some Intrinsic Characterizations of Besov-Triebel-Lizorkin-Morrey-type Spaces on Lipschitz Domains

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

Improving the Regularity of Vector Fields

The Frobenius Theorem for Log-Lipschitz Subbundles

A Counterexample to Ck-regularity for the Newlander-Nirenberg Theorem

On $\partial$ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates

A universal $\partial$ solution operator on nonsmooth strongly pseudoconvex domains

Sobolev and Hölder estimates for homotopy operators of the $\partial$ -equation on convex domains of finite multitype

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

A Counterexample to $C^{k}$ -regularity for the Newlander-Nirenberg Theorem