Hardy-type inequalities via convexity

Abstract

Abstract.A recently discovered Hardy-Pólya type inequality described by a convex function is considered and further developed both in weighted and unweighted cases. Also some corresponding multidimensional and reversed inequalities are pointed out. In particular, some new multidimensional Hardy and Pólya-Knopp type inequalities and some new integral inequalities with general integral operators (without additional restrictions on the kernel) are derived.Mathematics subject classification (2000): 26D10, 26D15.

Multidimensional Hardy-type inequalities with general kernels

“…[3] and [6]). In particular, our results further generalize and complement some recent results in [4].…”

“…For the case n = 1 Proposition 2.1 (i) coincides with Theorem 4.1 in [4]. Moreover, for the case k ≡ 1 in Proposition 2.1 we obtain Proposition 2.1 in [8].…”

Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

“…More general Hardy integral inequalities have been studied in continuous cases. We notice only [2][3][4][5][6] and the references therein.…”

Some new refinements of strengthened Hardy and Pólya–Knopp′s inequalities

“…in the monographs [13,22,23,25,26,27,28], expository papers [6,17,21], and the references cited therein. Besides, here we also emphasize the papers [2,4,5,7,8,9,18,19,24,29,32,33], all of which to some extent have guided us in the research we present here.…”