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- W2101882684 abstract "Abstract Let an almost everywhere positive function Φ be convex for p >1 and p <0, concave for p ∈(0,1), and such that Ax p ≤Φ( x )≤ Bx p holds on $mathbb {R}_{+}$ for some positive constants A ≤ B . In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve $Phi ( int _0^{x_1} cdots int _0^{x_n} f(t ),dt )$ instead of $[ int _0^{x_1} cdots int _0^{x_n} f(t ) , dt ]^p$ , while the corresponding right-hand sides remain as in the classical Hardy’s inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature." @default.
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- W2101882684 date "2008-04-01" @default.
- W2101882684 modified "2023-10-18" @default.
- W2101882684 title "MULTIDIMENSIONAL HARDY-TYPE INEQUALITIES VIA CONVEXITY" @default.
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- W2101882684 doi "https://doi.org/10.1017/s0004972708000245" @default.
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