2015/08/19 by Zhong-Wei Liao, Liao, Zhong-Wei
Computer Science · Engineering · Mathematics · #26D10 #34L15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in engineering #Spectral Theory in Mathematical Physics #math.FA #msc:26D10 #msc:34L15
paper · pdf · doi:10.48550/arxiv.1508.04601
23 pages
arxiv created 2015/08/19 · openalex publication_date 2015/08/19 · arxiv updated 2015/08/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint (ND-case). Based on the dual method, it can be translated into the case vanishing at left endpoint (DN-case). Secondly, the condition is the case that the sequences vanish at two endpoints (DD-case). The third type of condition is the generality of the mean zero condition (NN-case), which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.