Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson matrices. This problem is considered by some authors like Bennett, Jamson and the first author on sequence spaces and weighted sequence spaces for some kind of matrix operators. Also, this study is an extension of paper by Chang-Pao Chen, Dah-Chin Luor and Zong-Yin Ou.