论文标题
改善了具有一类重量的Hardy不平等现象
Improved Hardy inequalities with a class of weights
论文作者
论文摘要
\在本文中开始{摘要}，我们说明了潜在的$ v $条件，以使改进的不平等与重量\ begin \ begin {qore*} \ begin {split} c_ {n，μ} \ int _ {\ r^n} \ int _ {\ r^n} v \，φ^2μ（x）dx \\＆\ le \ le \ le \ int _ {\ r^n} | \ nabla ibla或$φ$在加权的Sobolev空间中，用于重量功能$μ$的一般类型。还给出了一些当地改善的耐力不平等。为了获得结果，我们使用广义矢量字段方法。 \ end {摘要}
\begin{abstract} In the paper we state conditions on potentials $V$ to get the improved Hardy inequality with weight \begin{equation*} \begin{split} c_{N,μ}\int_{\R^N}\frac{φ^2}{|x|^2}μ(x)dx&+ \int_{\R^N}V\,φ^2μ(x)dx \\&\le \int_{\R^N}|\nabla φ|^2μ(x)dx +K_1 \int_{\R^N} φ^2μ(x)dx, \end{split} \end{equation*} for functions $φ$ in a weighted Sobolev space and for weight functions $μ$ of a quite general type. Some local improved Hardy inequalities are also given. To get the results we use a generalized vector field method. \end{abstract}
