García del Amo, Alejandro On reverse Hardy’s inequality. (English) Zbl 0816.26006 Collect. Math. 44, No. 1-3, 115-123 (1993). The author, following C. J. Neugebauer [Publ. Mat., Barc. 35, No. 2, 429-447 (1991; Zbl 0746.42014)], studies a converse of Hardy’s inequality with weights, valid for non-increasing functions. The argument is based on an extension of the Riesz convexity theorem to operators that act on non-increasing functions.{Reviewer’s remark: A general theory of interpolation with respect to cones was developed by Sagher, including interpolation of operators acting on \(L^ p\) spaces restricted to non-increasing functions [cf. Y. Sagher, Stud. Math. 44, 239-252 (1972; Zbl 0258.42005); ibid. 41, 169-181 (1972; Zbl 0258.42004); Proc. Conf. Oberwolfach 1974, 169-180 (1974; Zbl 0322.46034)]. Reviewer: M.Milman (Boca Raton) Cited in 1 Document MSC: 26D15 Inequalities for sums, series and integrals 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B25 Maximal functions, Littlewood-Paley theory Keywords:converse of Hardy’s inequality; weights; Riesz convexity theorem; interpolation of operators Citations:Zbl 0746.42014; Zbl 0258.42005; Zbl 0258.42004; Zbl 0322.46034 PDFBibTeX XMLCite \textit{A. García del Amo}, Collect. Math. 44, No. 1--3, 115--123 (1993; Zbl 0816.26006) Full Text: EuDML