Aug 2026· 3 citations· ⚡ 1 influential· 16 references
Mathematics
Abstract
For every $n\geq 3$ we construct a bounded discontinuous map $u\in W^{1,n}(\mathbb{B}^n,\mathbb{R}^{n+2})$ solving an $n$-Laplace system with an antisymmetric potential $\Omega\in L^n$. This shows that a recent regularity result on $n$-Laplace systems with antisymmetric potentials in Lorentz spaces by the authors is sharp in the sense that we cannot move from Lorentz spaces to classical Lebesgue spaces. This gives in particular a negative answer to a question by Rivi\`ere.
We study properties of the calculus $\varphi\mapsto\varphi(A,B)$ for self-adjoint operators with commutator $[A,B]$ in the Schaten--von Neumann class $\boldsymbol{S}_p$. It turns out that this calculus defined on the Besov class $B_{\infty,1}^1({\Bbb R}^2)$ in the case $p\le2$ admits a commutator Lipschitz estimate and...
In this paper, it is proved that the commutator $\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0
Qin Zheng, Zun-Wei Fu· Communications in Mathematic...· 1 citation
We establish a noncommutative version of a familiar Johnson--Maurey--Schechtman--Tzafriri Theorem, by showing that for any $0<p<2$ and a (not necessarily semifinite) von Neumann algebra $\mathcal{M}$ on a separable Hilbert space, if a symmetric quasi-Banach function space $E(0,1) $ containing the function $t\mapsto t^{...
Jing-Hao Huang, M. Junge, F. Sukochev et al.· 1 citation
We consider the following singular Liouville equation $-\Delta v=\lambda V(x)|x|^2e^v \quad \text{in } B_1, \quad v=0 \quad \text{on } \partial B_1, $ where $B_1\subset\mathbb R^2$ is the unit disk, $\lambda>0$ is a small parameter, and $V$ is a positive smooth function. We first prove a non-degeneracy result for the b...
We establish a global uniqueness result at the critical Sobolev regularity for the isotropic Calder\'on problem in all dimensions $n\ge 4$. More precisely, for every $n\ge4$ and every bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, any real-valued, uniformly elliptic scalar conductivity $\gamma\in W^{1,n}(\Omega)...
Lu Chen, Yan Jiang, Hong-Yu Liu et al.· 1 citation
Let $\mathcal M$ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace $\tau$. We prove that, for every nonzero Banach space $Y$, the projective tensor product $L_1(\mathcal M,\tau)\widehat{\otimes}_{\pi}Y$ has the operator Daugavet property. Moreover, the witnessing operators may...
Jun-Xiang Qi, Qi Liu, Yong-Jin Li· 0 citations
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