5 papers
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…
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 . Using these, with…
Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators
Dachun Yang, Wen Yuan, Yirui Zhao
Let and with . In this article, we introduce a new family of lifted rough maximal operators $\{\mathcal{M…
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…
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…