论文标题
一维锋利的离散耐力 - 里希希不平等现象
One dimensional sharp discrete Hardy-Rellich inequalities
论文作者
论文摘要
在本文中，我们在$ \ mathbb {n} $上建立了离散的hardy-rellich不等式，并使用$Δ^\ frac {\ ell} {2} {2} $和最佳常数，对于任何$ \ ell \ geq 1 $。据我们所知，这些尖锐的不平等现象是$ \ ell \ geq 3 $的新不平等现象。我们的方法是使用加权平等，以使用变化的权重来使一些急剧的不平等现象，然后通过迭代来解决更高级别的情况。我们还提供与连续设置相同的常数，在$ \ mathbb {n} $上提供新的Hardy-Leray类型不平等。此外，主要想法也适用于通用图或$ \ ell^p $设置。
In this paper, we establish discrete Hardy-Rellich inequalities on $\mathbb{N}$ with $Δ^\frac{\ell}{2}$ and optimal constants, for any $\ell \geq 1$. As far as we are aware, these sharp inequalities are new for $\ell \geq 3$. Our approach is to use weighted equalities to get some sharp Hardy inequalities using shifting weights, then to settle the higher order cases by iteration. We provide also a new Hardy-Leray type inequality on $\mathbb{N}$ with the same constant as the continuous setting. Furthermore, the main ideas work also for general graphs or the $\ell^p$ setting.
