利用Hölder不等式刻画$L_p$ -模

Hilbert $C^*$-模中的凸不等式

Convex inequalities in Hilbert $C^*$-modules

本文将H$"o$lder-McCarty不等式中的凸不等式推广至Hilbert $C^*$-模，并研究该情形下的相关不等式。

Conditional $h$-convexity with applications

In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's inequality, arithmetic-geometric mean inequality, Chrystal inequality, and H$\ddot{o}$lder-McCarthy inequality. Many of the other inequalities can be refined by applying this new notion.

Sobolev 空间与度量空间上常函数的刻画

Characterisations of Sobolev spaces and constant functions over metric spaces

本文在满足Poincaré不等式的度量空间中，通过均振荡给出了Sobolev空间的新刻画，并扩展了常函数的特征，同时探讨了共轭算子的映射性质。

Characterisation of homogeneous fractional Sobolev spaces

Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\uı spaces $\mathcal{D}^{s,p} (\mathbb{R}^n)$ and their embeddings, for $s \in (0,1]$ and $p\ge 1$. They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo-Slobodecki\uı seminorms. For $s\,p < n$ or $s = p = n = 1$ we show that $\mathcal{D}^{s,p}(\mathbb{R}^n)$ is isomorphic to a suitable function space, whereas for $s\,p \ge n$ it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we…

关于通过热核的同质类型狄利克雷空间

On Dirichlet Spaces of Homogeneous Type Via Heat Kernel

本文提出了一种基于热核的同质类型狄利克雷空间框架，用于分析带限函数在不同空间中的表示和分解。

振荡范数的$A_\infty$不变性与交换子的Schatten刻画

$A_\infty$-invariance of oscillatory norms, and Schatten characterisations of commutators

本文扩展已有交换子Schatten类刻画的抽象框架，引入$A_\infty$等价测度对放宽正则性假设，用实变调和分析方法复现并简化了Bessel-Riesz变换交换子的相关刻画结果。