Hardy's Inequality with Three Measures
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 233-245

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Necessary and sufficient conditions are obtained for the fulfillment of a Hardy inequality with three $\sigma$-finite measures on the number axis.
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     author = {D. V. Prokhorov},
     title = {Hardy's {Inequality} with {Three} {Measures}},
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D. V. Prokhorov. Hardy's Inequality with Three Measures. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 233-245. http://geodesic.mathdoc.fr/item/TM_2006_255_a17/