Geodesic
Iterated Integral Operators on the Cone of Monotone Functions
Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 454-466.

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Criteria for the boundedness of sublinear integral two-kernel operators of iterated type on cones of monotone functions in Lebesgue spaces on the real semiaxis are given.
Keywords: Hardy-type inequality, weighted Lebesgue space, sublinear integral operator. 
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V. D. Stepanov; G. È. Shambilova. Iterated Integral Operators on the Cone of Monotone Functions. Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 454-466. http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a10/

[1] R. Oinarov, “Dvustoronnie otsenki normy nekotorykh klassov integralnykh operatorov”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 16, Tr. MIAN, 204, Nauka, M., 1993, 240–250 | MR | Zbl

[2] G. E. Shambilova, “Vesovye neravenstva dlya odnogo klassa kvazilineinykh integralnykh operatorov na konuse monotonnykh funktsii”, Sib. matem. zhurn., 55:4 (2014), 912–936 | MR | Zbl

[3] V. D. Stepanov, G. E. Shambilova, “Ogranichennost kvazilineinykh integralnykh operatorov na konuse monotonnykh funktsii”, Sib. matem. zhurn., 57:5 (2016), 1131–1155 | DOI | MR | Zbl

[4] V. D. Stepanov, G. E. Shambilova, “On the boundedness of quasilinear integral operators of iterated type with Oinarov's kernels on the cone of monotone functions”, Eurasian Math. J., 8:2 (2017), 47–73 | MR

[5] D. V. Prokhorov, V. D. Stepanov, “O vesovykh neravenstvakh Khardi v smeshannykh normakh”, Teoriya funktsii i uravneniya matematicheskoi fiziki, Tr. MIAN, 283, MAIK «Nauka/Interperiodika», M., 2013, 155–170 | DOI | MR

[6] D. V. Prokhorov, V. D. Stepanov, “Vesovye neravenstva dlya kvazilineinykh integralnykh operatorov na poluosi i prilozheniya k prostranstvam Lorentsa”, Matem. sb., 207:8 (2016), 135–162 | DOI | MR | Zbl

[7] D. V. Prokhorov, “Ob odnom klasse vesovykh neravenstv, soderzhaschikh kvazilineinye operatory”, Funktsionalnye prostranstva, teoriya priblizhenii, smezhnye razdely matematicheskogo analiza, Tr. MIAN, 293, MAIK «Nauka/Interperiodika», M., 2016, 280–295 | DOI | MR

[8] A. Gogatishvili, V. D. Stepanov, “Reduktsionnye teoremy dlya vesovykh integralnykh neravenstv na konuse monotonnykh funktsii”, UMN, 68:4 (412) (2013), 3–68 | DOI | MR | Zbl

[9] L.-E. Persson, G. E. Shambilova, V. D. Stepanov, “Hardy-type inequalities on the weighted cones of quasi-concave functions”, Banach J. Math. Anal., 9:2 (2015), 21–34 | DOI | MR | Zbl

[10] V. I. Burenkov, R. Oinarov, “Necessary and sufficient conditions for boundedness of the Hardy-type operator from a weighted Lebesgue space to a Morrey-type space”, Math. Inequal. Appl., 16:1 (2013), 1–19 | MR | Zbl