caa a22 4500 605508518 CHVBK 20210128100637.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-013-0230-x doi (NATIONALLICENCE)springer-10.1007/s00010-013-0230-x Unifying inequalities of Hardy, Copson, and others [Elektronische Daten] [H. Carley, P. Johnson Jr., R. Mohapatra] In order to provide an alternative proof to an inequality of Hilbert, Hardy proved $$\sum_{n=0}^{\infty} \left((n+1)^{-1} \sum_{k=0}^{n}x_k\right)^p \leq\left(\frac{p}{p-1} \right)^p\sum_{n=0}^\infty x_n^p. $$ ∑ n = 0 ∞ ( n + 1 ) - 1 ∑ k = 0 n x k p ≤ p p - 1 p ∑ n = 0 ∞ x n p . This inequality and its relatives triggered research activity concerning norm inequalities including new inequalities by Copson and Levinson. In this paper, three theorems are established from which related inequalities of Hardy, Copson, and Levinson and various extensions are deduced as corollaries. Springer Basel, 2013 Carley H. Department of Mathematics, New York City College of Technology-CUNY, 11201, Brooklyn, NY, USA aut Johnson Jr. P. Department of Math and Statistics, Auburn University, 36849, Auburn, AL, USA aut Mohapatra R. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA aut Aequationes mathematicae Springer Basel 89/3(2015-06-01), 497-510 0001-9054 89:3<497 2015 89 10 https://doi.org/10.1007/s00010-013-0230-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-013-0230-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carley H. Department of Mathematics, New York City College of Technology-CUNY, 11201, Brooklyn, NY, USA aut NATIONALLICENCE 700 1- Johnson Jr P. Department of Math and Statistics, Auburn University, 36849, Auburn, AL, USA aut NATIONALLICENCE 700 1- Mohapatra R. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 497-510 0001-9054 89:3<497 2015 89 10