论文标题
$ l^{1} $ norm in vector字段中的Stein-Weiss不平等
Stein-Weiss inequality in $L^{1}$ norm for vector fields
论文作者
论文摘要
在这项工作中，我们调查了限制案例$ p = 1 $的经典Stein- Weiss不平等现象的Riesz电位。我们为与Cocanceling Operators相关的特殊类矢量字段的表征提出了ARXIV介绍的Cocanceling Operators：1104.0192。作为应用程序，我们恢复了文献中发现的一些Div-Curl不平等。此外，我们在标量案例中讨论了具有一般权重的两重量不等式，从而将Sawyer的先前结果扩展到了这种情况。
In this work, we investigate the limit case $p=1$ of the classical Stein--Weiss inequality for the Riesz potential.We present a characterization for a special class of vector fields associated to cocanceling operators introduced by Van Schaftingen in arXiv:1104.0192. As an application, we recover some div-curl inequalities found in the literature. In addition, we discuss a two-weight inequality with general weights in the scalar case, extending the previous result of Sawyer to this case.
