Kaijser, Sten; Nikolova, Ludmila; Persson, Lars-Erik; Wedestig, Anna Hardy-type inequalities via convexity. (English) Zbl 1083.26013 Math. Inequal. Appl. 8, No. 3, 403-417 (2005). It was noticed by S. Kaijser, L.-E. Persson and A. Öberg [see their paper, “On Carleman and Knopp’s inequalities”, J. Approximation Theory 117, No. 1, 140–151 (2002; Zbl 1049.26014)] that the Hardy-type inequalities can be extended to \[ \int_{0}^{\infty}\Phi\left( \frac{1}{x}\int_{0}^{x}f(t)\,dt\right) \frac {dx}{x}\leq\int_{0}^{\infty}\Phi\left( f(x)\right) \frac{dx}{x} \] where \(\Phi\) is a convex function on \(\left( 0,\infty\right) .\) The paper under review contains further developments in the weighted and multidimensional framework. Also, some reversed inequalities are pointed out. Reviewer: Constantin Niculescu (Craiova) Cited in 1 ReviewCited in 38 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 26A51 Convexity of real functions in one variable, generalizations Keywords:Hardy inequality; Pólya-Knopp inequality; Hardy type operators Citations:Zbl 1049.26014 PDFBibTeX XMLCite \textit{S. Kaijser} et al., Math. Inequal. Appl. 8, No. 3, 403--417 (2005; Zbl 1083.26013) Full Text: DOI