Author

Da-Chun Yang

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Preprint Oct 2026

Sharp Poincar\'e Inequalities for Families of Nonlocal Nonconvex Functionals

Let $N\in\mathbb N$, $p\in[1,\infty)$, and $Q_0:=(0,1)^N$. In this article, we establish sharp Poincar\'e inequalities for the nonlocal nonconvex functionals $$ \Phi_{\lambda,p}^\gamma(g;Q_0) :=\lambda^p\iint_{\{(x,y)\in Q_0^2:\,x\ne y,\,|g(x)-g(y)|>\lambda|x-y|^{1+\frac{\gamma}{p}}\}} |x-y|^{\gamma-N}\,dx\,dy, $$ wher...

Feng Dai, Da-Chun Yang, Wen Yuan et al. · 0 citations

Preprint Sep 2026

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

Let $\alpha\in(0,n)$, $p\in(1,\frac{n}{\alpha})$, $q:=\frac{np}{n-\alpha p}$, and $W\in\mathscr A_{p,q}$. We establish the following quantitative matrix-weighted estimate for the fractional integral $I_\alpha$: for any $\vec{f}\in L^p(W^p)$, \begin{align*} \left\|I_\alpha\vec f\right\|_{L^q(W^q)} \lesssim[W]_{\mathscr...

Da-Chun Yang, Wen Yuan, Ming-Dong Zhang · 0 citations

Preprint Aug 2026

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

Given a complete doubling metric measure space $(X,\rho,\mu)$ supporting a Poincar\'e inequality, we prove weak-type characterizations of the Sobolev space $\dot{W}^{1,p}(\mu)$ and the space of functions of bounded variation, achieving a full analogy in general Poincar\'e spaces with the Euclidean results of Brezis et...

T. Hytönen, Da-Chun Yang, Wen Yuan et al. · 2 citations