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MR2213710 26D15 (42B35 47B38)
Persson, L.-E.; Stepanov, V. D.; Ushakova, E. P. Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions. Proc. Amer. Math. Soc. 134 (2006), no. 8, 2363–2372.
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