论文标题
关于Hardy和Copson不平等的改善
On the improvements of Hardy and Copson inequalities
论文作者
论文摘要
在当前的工作中，我们在一个维度上重新审视了离散的Hardy不平等现象的最新改善，并以其最佳性建立了扩展的改进的离散Hardy的不平等。我们还研究了一维离散的科普森的不平等（E.T. Copson，\ emph {关于一系列积极术语的注释}，J。LondonMath。Soc。，2（1927），9-12。），并在特定案例中实现了相同的改进。此外，我们研究了一些基本结构，例如完整性，kötoeplitz二元性，可分离性等，这些序列空间源自一维的改善的离散耐受性和科普森不平等的序列空间。
In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 9-12.), and achieve an improvement of the same in a particular case. Further, we study some fundamental structures such as completeness, Köthe-Toeplitz duality, separability, etc. of the sequence spaces which originated from the improved discrete Hardy and Copson inequalities in one dimension.
