Abstract
In this paper, we prove some properties of weighted Cesàro and Copson sequences spaces by establishing some factorization theorems. The results lead to two-sided norm discrete inequalities with best possible constants and also give conditions for the boundedness of the generalized discrete weighted Hardy and Copson operators.
Highlights
The study of discrete spaces in functional and harmonic analysis has become an active field of research
We study the structure of the weighted Cesàro and Copson sequence spaces
[7] Barza et al extended the results proved in [5] and proved some factorization theorems for the Cesàro and Copson functions spaces with weights
Summary
The study of discrete spaces in functional and harmonic analysis has become an active field of research. In [26] Shiue investigated this problem for the first time, and later it was analyzed by Leibowitz [20] and Jagers [16], and for dual spaces of Cesàro space of sequences and functions, we refer to [29] They proved that cesp(N) is a separable reflexive Banach space for 1 < p < ∞, and it does have the fixed point property, and if 1 < p < q < ∞, cesp ⊂ cesq with continuous strict embedding. We develop a new technique to study the structure of weighted Cesàro and Copson sequences spaces and prove some factorization theorems.
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