Discrete Weighted Hardy Inequalities with Different Kinds of Boundary Conditions  

作　　者：Zhong Wei LIAO 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2016年第9期993-1013,共21页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11131003);the “985” project from the Ministry of Education in China

摘　　要：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.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.

关 键 词：Weighted Hardy inequality one-side boundary condition vanishing at two endpoints mean zero basic estimates dual method splitting technique 

分 类 号：O178[理学—数学] TP391.72[理学—基础数学]