5 papers
Sharp Truncated Difference Estimates for Nonlocal Nonconvex Functionals Defined by Superlevel Sets
Feng Dai, Dachun Yang, Wen Yuan +1
Let and . In this article, we consider a family of nonlocal nonconvex functionals with a real parameter and est…
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 and establish the quantitative boundedness of several operators on local matrix-we…
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 supporting a Poincaré inequality, we prove weak-type characterizations of the Sobolev space and the spac…
Besov--Triebel--Lizorkin-Type Spaces with Matrix Weights
Fan Bu, Tuomas Hytönen, Dachun Yang +1
Introduced by A. Volberg, matrix weights provide a suitable generalization of Muckenhoupt weights from the classical theory. In our previous work, we esta…
Sharp Weighted Cohen--Dahmen--Daubechies--DeVore Inequality with Applications to (Weighted) Critical Sobolev Spaces, Gagliardo--Nirenberg Inequalities, and Muckenhoupt Weights
Yinqin Li, Dachun Yang, Wen Yuan +2
In this article, we establish a quantitative weighted variant of a far-reaching inequality obtained by A. Cohen, W. Dahmen, I. Daubechies, and R. DeVore in 2003, whose dependence o…