Geodesic
On a~weighted inequality for a~Hardy-type operator
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 216-223.

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A new criterion is obtained for a weighted inequality to hold in the Lebesgue spaces for a Hardy-type integral operator with Oinarov's kernel. 
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     author = {D. V. Prokhorov},
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D. V. Prokhorov. On a~weighted inequality for a~Hardy-type operator. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 216-223. http://geodesic.mathdoc.fr/item/TM_2014_284_a14/

[1] Kantorovich L.V., Akilov G.P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl

[2] Bloom S., Kerman R., “Weighted norm inequalities for operators of Hardy type”, Proc. Amer. Math. Soc., 113:1 (1991), 135–141 | DOI | MR | Zbl

[3] Oinarov R., “Dvustoronnie otsenki normy nekotorykh klassov integralnykh operatorov”, Tr. MIAN, 204, 1993, 240–250 | Zbl

[4] Stepanov V.D., “Weighted norm inequalities of Hardy type for a class of integral operators”, J. London Math. Soc. Ser. 2, 50:1 (1994), 105–120 | DOI | MR | Zbl

[5] Lai Q., “Weighted modular inequalities for Hardy type operators”, Proc. London Math. Soc. Ser. 3, 79:3 (1999), 649–672 | DOI | MR | Zbl

[6] Gol'dman M.L., Heinig H.P., Stepanov V.D., “On the principle of duality in Lorentz spaces”, Can. J. Math., 48:5 (1996), 959–979 | DOI | MR | Zbl

[7] Lomakina E., Stepanov V., “On the Hardy-type integral operators in Banach function spaces”, Publ. Mat., 42:1 (1998), 165–194 | DOI | MR | Zbl

[8] Mazya V.G., Prostranstva S.L. Soboleva, Izd-vo LGU, L., 1985 | MR | Zbl

[9] Sinnamon G.J., “Weighted Hardy and Opial-type inequalities”, J. Math. Anal. Appl., 160:2 (1991), 434–445 | DOI | MR | Zbl

[10] Sinnamon G., Stepanov V.D., “The weighted Hardy inequality: New proofs and the case $p=1$”, J. London Math. Soc. Ser. 2, 54:1 (1996), 89–101 | DOI | MR | Zbl