6 papers
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…
Stability for the Affine Sobolev Inequality and its Critical Points for
Rupert L. Frank, Yinqin Li, Dachun Yang
We prove stability for the affine Sobolev inequality for exponents with best possible norm and best possible stability exponent. We also show a corresponding result for c…
Real-variable theory of function spaces with operator-valued weights in Banach spaces
Tuomas P. Hytönen, Yinqin Li, Dachun Yang +1
While the theory of matrix-weighted function spaces is well established, the majority of previous results in the infinite-dimensional operator-valued setting deal with "no go" theo…
A Sharp Localized Weighted Inequality Related to Gagliardo and Sobolev Seminorms and Its Applications
Pingxu Hu, Yinqin Li, Dachun Yang +1
In this article, we establish a nearly sharp localized weighted inequality related to Gagliardo and Sobolev seminorms, respectively, with the sharp -weight constant or with th…
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…
Sharp Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces
Pingxu Hu, Yinqin Li, Dachun Yang +2
Let be a ball Banach function space on , , , and denote the {\rm th} order difference. In this article, under some m…