Persson, Lars-Erik; Popova, Olga V.; Stepanov, Vladimir D. Two-sided Hardy-type inequalities for monotone functions. (English) Zbl 1217.26034 Complex Var. Elliptic Equ. 55, No. 8-10, 973-989 (2010). Some 2-sided Hardy-type inequalities on the cones of monotone functions with positive \(\sigma\)-finite Borel measure are established. As an application, the equivalence of a discrete Hardy inequality with a simple inequality on monotone sequences is obtained. Reviewer: Wing-Sum Cheung (Hong Kong) Cited in 5 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Hardy-type Inequalities PDFBibTeX XMLCite \textit{L.-E. Persson} et al., Complex Var. Elliptic Equ. 55, No. 8--10, 973--989 (2010; Zbl 1217.26034) Full Text: DOI References: [1] Kufner A, About its History and Some Related Results (2007) · Zbl 1213.42001 [2] Kufner A, Weighted Inequalities of Hardy Type (2003) [3] Opic B, Pitman Research Notes in Mathematics , Series 219 (1990) [4] DOI: 10.1007/s00208-005-0678-7 · Zbl 1119.26018 [5] Bennett G, Houston J. Math. 31 pp 541– (2005) [6] Bergh J, Acta Sci. Math. (Szeged) 59 pp 221– (1994) [7] Carro MJ, Math. Inequal. Appl. 4 pp 397– (2001) [8] Goldman ML, Proc. Steklov Inst. Math. 232 pp 109– (2001) [9] Johansson M, Math. Inequal. Appl. 11 pp 393– (2008) [10] DOI: 10.1090/S0002-9939-06-08403-6 · Zbl 1093.26023 [11] Sawyer E, Studia Math. 96 pp 145– (1990) [12] Sinnamon G, Collect. Math. 54 pp 181– (2003) [13] Sinnamon G, Function Spaces and Nonlinear Analysis pp 292– (2005) [14] Sinnamon G, J. London Math. Soc. 54 pp 89– (1996) [15] DOI: 10.2307/2154450 · Zbl 0786.26015 [16] DOI: 10.1112/jlms/s2-48.3.465 · Zbl 0837.26011 [17] Prokhorov DV, Proc. Steklov Inst. Math. 255 pp 233– (2007) [18] Royden HL, Real Analysis,, 3. ed. (1988) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.