论文标题
$ \ dot w^{1，p}（\ mathbb r^d）$的特征
A characterization of $\dot W^{1,p}(\mathbb R^d)$
论文作者
论文摘要
对于$ 1 <p <\ infty $，我们给出了Sobolev空间$ \ dot w^{1，p}（\ mathbb r^d）$的表征，以变化中心和半径的函数的振荡。我们的工作既是通过对具有单数积分运算符的换向因子的痕量理想特性以及Nguyen的工作以及Brezis，van Schaftingen和Yung对Sobolev空间无衍生性特征的研究来激励的。
For $1<p<\infty$ we give a characterization of the Sobolev space $\dot W^{1,p}(\mathbb R^d)$ in terms of the oscillations of a function on balls of varying centers and radii. Our work is motivated both by the study of trace ideal properties of commutators with singular integral operators and by work of Nguyen and by Brezis, Van Schaftingen and Yung on derivative-free characterizations of Sobolev spaces.
