Persson, L.-E.; Popova, O. V.; Stepanov, V. D. Weighted Hardy-type inequalities on the cone of quasi-concave functions. (English) Zbl 1291.39049 Math. Inequal. Appl. 17, No. 3, 879-898 (2014). Summary: The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz \(\Gamma \)-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters \(q\geq 1 , p > 0\) and sufficient conditions for the rest of the range of parameters. Cited in 5 Documents MSC: 39B62 Functional inequalities, including subadditivity, convexity, etc. 45P05 Integral operators Keywords:Hardy operator; Hardy-type inequality; weight; measure; Lorentz space; concave function; quasi-concave function PDFBibTeX XMLCite \textit{L. E. Persson} et al., Math. Inequal. Appl. 17, No. 3, 879--898 (2014; Zbl 1291.39049) Full Text: DOI