Xue Xiaomin, Li Fushan
1School of Mathematical Sciences, Qufu Normal University, Qufu, P.R. China.
2Center for Teaching Research and Evaluation, Qufu Normal University, Qufu, P.R. China.
J Inequal Appl. 2018;2018(1):330. doi: 10.1186/s13660-018-1922-5. Epub 2018 Nov 28.
In this paper, we refine the proof of Hardy's inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy's inequality from two aspects. That is to say, we extend the integral estimation function from to with suitable and extend the space dimension from to . Hardy's inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) is the special case of our results.
在本文中，我们完善了（见埃文斯所著《偏微分方程》，2010年；哈代所著《不等式》，1952年）中哈代不等式的证明，并从两个方面对哈代不等式进行了推广。也就是说，我们将积分估计函数从 推广到具有适当 的 ，并将空间维度从 推广到 。（见埃文斯所著《偏微分方程》，2010年；哈代所著《不等式》，1952年）中的哈代不等式是我们结果的特殊情况。
