Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Persson, L.-E.; Stepanov, V.; Ushakova, E.

doi:10.1090/S0002-9939-06-08403-6

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions
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by L.-E. Persson, V. D. Stepanov and E. P. Ushakova PDF

Proc. Amer. Math. Soc. 134 (2006), 2363-2372 Request permission

Abstract:

Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel $k(x,y)$, are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

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