7 papers
Compactness and Its Applications of Sobolev Spaces Associated with Ball Banach Function Spaces
Xiaosheng Lin, Dachun Yang, Wen Yuan +1
Let be a bounded Lipschitz domain in , and be a ball Banach function space on In this article, under some mild assu…
A Counterexample to the Necessity of the Vanishing Carleson Condition for VMO Poisson Kernels
Xiaosheng Lin, Dachun Yang, Sibei Yang +2
In [Problem 3.2.23, CBMS Regional Conference Series in Mathematics 83, 1994], Kenig asked whether the vanishing Carleson condition is the necessary and sufficient for the logarithm…
A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions
Xiaosheng Lin, Dachun Yang, Sibei Yang +2
Let . In this article, we show that there exists a bounded domain such that, for any given $s\in(1,2)\setminus\{\frac32\…
Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces
Feng Dai, Eero Saksman, Dachun Yang +2
Let denote the inhomogeneous Lipschitz space of order on . This article characterizes the distance $d(f, V)_{Î_s}: = \inf_{g\in V} \|f-g\|_{Î…
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…
Difference and Wavelet Characterizations of Distances from Functions in Lipschitz Spaces to Their Subspaces
Feng Dai, Eero Saksman, Dachun Yang +2
Let denote the Lipschitz space of order on , which consists of all such that, for some constant $L\in(0,\infty…