Xiaosheng Lin

activity

20212026

most citedBrezis--Van Schaftingen--Yung Formulae in Ball Banach Function Spaces with Applications to Fractional Sobolev and Gagliardo--Nirenberg Inequalities

2 citations · 2 across the 9 of their papers we have counts for

collaborators

9 papers

math.FA2026

Local Hardy Spaces Associated with Operators and Ball Quasi-Banach Function Spaces on Doubling Metric Measure Spaces and Their Applications

Xiaosheng Lin, Xiaotian Zhu

Let $(X, d, μ)$ be a doubling metric measure space, $X$ a ball quasi-Banach function space on $X$ , and $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X…

math.CA2026

$Γ$ -Convergence of Weak-Type Nonlocal Functionals on Bounded Domains

Xiaosheng Lin, Dachun Yang, Sibei Yang +2

Let $N \geq 1$ , $p \in [1, \infty)$ , $γ \in (0, \infty)$ , and $Ω \subset R^{N}$ be a bounded open interval when $N = 1$ or a bounded Lipschitz domain when $N \geq 2$ . For any $λ\in(0,\infty)…

math.FA2026

Compactness and Its Applications of Sobolev Spaces Associated with Ball Banach Function Spaces

Xiaosheng Lin, Dachun Yang, Wen Yuan +1

Let $N \in N \cap [2, \infty),$ $Ω$ be a bounded Lipschitz domain in $R^{N}$ , and $X (Ω)$ be a ball Banach function space on $Ω.$ In this article, under some mild assumpt…

math.AP2026

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…

math.AP2026

A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions

Xiaosheng Lin, Dachun Yang, Sibei Yang +2

Let $n \in N \cap [2, \infty)$ . In this article, we show that there exists a bounded $C^{1}$ domain $Ω \subset R^{n}$ such that, for any given $s\in(1,2)\setminus\{\frac32\}…

math.FA2023

Hardy Spaces Associated with Non-Negative Self-Adjoint Operators and Ball Quasi-Banach Function Spaces on Doubling Metric Measure Spaces and Their Applications

Xiaosheng Lin, Dachun Yang, Sibei Yang +1

Let $(X, d, μ)$ be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, $L$ a non-negative self-adjoint operator on $L^{2} (X)$ satisfying the…

math.FA2022

Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces

Xiaosheng Lin, Dachun Yang, Sibei Yang +1

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $R^{n}$ and $X$ a ball quasi-Banach function space on…

math.FA2021

Poincaré Inequality Meets Brezis--Van Schaftingen--Yung Formula on Metric Measure Spaces

Feng Dai, Xiaosheng Lin, Dachun Yang +2

Let $(X, ρ, μ)$ be a metric measure space of homogeneous type which supports a certain Poincaré inequality. Denote by the symbol $\mathcal{C}_{\mathrm{c}}^\ast(\mathcal{X…

math.CA2021★ 2 cited

Brezis--Van Schaftingen--Yung Formulae in Ball Banach Function Spaces with Applications to Fractional Sobolev and Gagliardo--Nirenberg Inequalities

Feng Dai, Xiaosheng Lin, Dachun Yang +2

Let $X$ be a ball Banach function space on $R^{n}$ . In this article, under some mild assumptions about both $X$ and the boundedness of the Hardy--Littlewood maximal operato…

Local Hardy Spaces Associated with Operators and Ball Quasi-Banach Function Spaces on Doubling Metric Measure Spaces and Their Applications

Γ-Convergence of Weak-Type Nonlocal Functionals on Bounded Domains

Compactness and Its Applications of Sobolev Spaces Associated with Ball Banach Function Spaces

A Counterexample to the Necessity of the Vanishing Carleson Condition for VMO Poisson Kernels

A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions

Hardy Spaces Associated with Non-Negative Self-Adjoint Operators and Ball Quasi-Banach Function Spaces on Doubling Metric Measure Spaces and Their Applications

Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces

Poincaré Inequality Meets Brezis--Van Schaftingen--Yung Formula on Metric Measure Spaces

Brezis--Van Schaftingen--Yung Formulae in Ball Banach Function Spaces with Applications to Fractional Sobolev and Gagliardo--Nirenberg Inequalities

$Γ$ -Convergence of Weak-Type Nonlocal Functionals on Bounded Domains