论文标题
Hardy的不平等不平等，剩余的剩余不平等
Hardy's inequalities with non-doubling weights and sharp remainders
论文作者
论文摘要
在本文中，我们应建立n维Hardy的不平等现象，其重量功能是到边界距离的距离，而边界为$ r^n $的边界为$ c^2 $ class有限域。这项工作本质上是基于一个尺寸加权的Hardy的不平等，具有单方面的边界条件和急剧的剩余。作为权重，我们承认可能会以无限顺序消失或炸毁的相当一般的人，例如$ e^{ - 1/t} $或$ e^{1/t} $ at $ t = 0 $在一个维度的情况下。
In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on one dimensional weighted Hardy's inequalities with one-sided boundary condition and sharp remainders. As weights we admit rather general ones that may vanish or blow up in infinite order such as $e^{-1/t}$ or $e^{1/t}$ at $t=0$ in one dimensional case.
