Norm Dynamic Inequalities and Theorems of Factorization of Weighted Cesàro and Copson Spaces

Abstract

In this paper, we establish some factorization theorems for weighted Cesaro and Copson spaces, obtain two sided norm dynamic inequalities, and give conditions for the boundedness of the Hardy and Copson dynamic operators on the weighted space $$L_{\lambda }^{p}({\mathbb {T}})$$ . We obtain, as special cases, the classical integral inequalities on $${\mathbb {R}}$$ and the discrete inequalities on $${\mathbb {N}}$$ .