Bull Braz Math Soc, New Series (2020) 51:915–936 https://doi.org/10.1007/s00574-019-00181-w Norm Dynamic Inequalities and Theorems of Factorization of Weighted Cesàro and Copson Spaces S. H. Saker 1 · M. M. Abuelwafa 1 · Donal O’Regan 2 · R. P. Agarwal 3 Received: 8 February 2019 / Accepted: 8 November 2019 / Published online: 18 November 2019 © Sociedade Brasileira de Matemática 2019 Abstract In this paper, we establish some factorization theorems for weighted Cesàro and Cop- son 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 p λ (T). We obtain, as special cases, the classical integral inequalities on R and the discrete inequalities on N. Keywords Factorization · Hardy’s dynamic operator · Lebesgue spaces · Cesàro spaces · Copson spaces · Time scales Mathematics Subject Classification Primary 26D20; Secondary 46B25 · 47G10 · 47J20 1 Introduction In Bennett (1996) Bennett described a new way of looking at the classical Hardy inequality B R. P. Agarwal Ravi.Agarwal@tamuk.edu S. H. Saker shsaker@mans.edu.eg M. M. Abuelwafa room949@yahoo.com Donal O’Regan donal.oregan@nuigalway.ie 1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 2 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland 3 Department of Mathematics, Texas A & M University, Kingsville, TX 78363, USA 123