Wen Yuan

activity

20242026

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8 papers · 1 filter

math.AP2026

Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets

Feng Dai, Dachun Yang, Wen Yuan +1

Let $N \in N$ and $p \in [1, \infty)$ . In this article, we consider a family ${Φ_{λ, p}^{γ}}_{λ \in (0, \infty)}$ of nonlocal nonconvex functionals with a real parameter $γ$ and est…

math.CA2026

Sharp Quantitative Matrix-Weighted Bounds for Fractional Integrals and Sobolev Inequalities

Dachun Yang, Wen Yuan, Mingdong Zhang

For $α \in (0, n)$ , $p \in (1, \frac{n}{α})$ , $q := \frac{n p}{n - α p}$ , and $W \in A_{p, q}$ , we obtain the following matrix-weighted boundedness of the fractional integral $I_{α}$ : for an…

math.CA2026

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Fan Bu, Dachun Yang, Wen Yuan

Let $T$ be a convolution Calderón--Zygmund operator satisfying Hytönen's non-degeneracy condition. We prove that, for every $p \in (1, \infty)$ and $m \geq 3$ , there exists a positive co…

math.FA2026

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Tuomas Hytönen, Dachun Yang, Wen Yuan +1

In this article, we give various real-variable properties of local Muckenhoupt matrix weights $W$ and establish the quantitative boundedness of several operators on local matrix-we…

math.FA2026

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Tuomas P. Hytönen, Dachun Yang, Wen Yuan +1

Given a complete doubling metric measure space $(X, ρ, μ)$ supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space $W ˙^{1, p} (μ)$ and the spac…

math.CA2026

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights

Fan Bu, Shuaijun Feng, Qingying Xue +2

Let $α \in R$ , $p \in (0, \infty)$ , and $q \in (0, \infty]$ . In this article, we develop a theory of matrix-weighted anisotropic Besov spaces associated with an expansive matrix $…

math.CA2026

Fractional Gagliardo--Nirenberg Inequalities: Pointwise Estimates,Sharp Asymptotics, and Optimal Target Spaces

Pingxu Hu, Yinqin Li, Dachun Yang +1

We establish two pointwise estimates for fractional difference operators, tracking explicitly the dependence of the constants on the smoothness index $s \in (0, 1)$ . Using these, with…

math.CA2026

Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators

Dachun Yang, Wen Yuan, Yirui Zhao

Let $n \in N \cap [2, \infty)$ and $Ω \in L^{1} (S^{n - 1})$ with $Ω \neq \equiv 0$ . In this article, we introduce a new family of lifted rough maximal operators $\{\mathcal{M}_…

Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets

Sharp Quantitative Matrix-Weighted Bounds for Fractional Integrals and Sobolev Inequalities

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents

Weak-type characterizations of Sobolev and bounded variation spaces on metric measure spaces

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix A∞​ Weights

Fractional Gagliardo--Nirenberg Inequalities: Pointwise Estimates,Sharp Asymptotics, and Optimal Target Spaces

Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights