Geodesic
Investigation of generalized Hardy inequality via a system of nonlinear differential equations in weighted Lebesgue spaces with mixed norm
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 16-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main goal of this paper is to found a criteria for two dimensional Hardy operator via a system of nonlinear differential equations in weighted Lebesgue spaces with mixed norm. In particular, it is proved that the weight functions that are the coefficients of a system of nonlinear differential equations are included in the estimate of the two-dimensional Hardy operator in this space. 
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     title = {Investigation of generalized {Hardy} inequality via a~system of nonlinear differential equations in weighted {Lebesgue} spaces with mixed norm},
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R. A. Bandaliev. Investigation of generalized Hardy inequality via a system of nonlinear differential equations in weighted Lebesgue spaces with mixed norm. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 16-26. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a2/

[1] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fiziki, Izd. LGU, L., 1950, 255 pp. | MR

[2] Sedov V. N., “Vesovye prostranstva. Teorema vlozheniya”, Dif. uravneniya, 8:8 (1972), 1452–1462 | MR | Zbl

[3] Sysoeva F. A., “Obobschenie nekotorogo neravenstva Khardi”, Izv. vuzov. Ser. mat., 49:6 (1965), 140–143 | MR | Zbl

[4] Nikolskii Yu. S., “K zadache Dirikhle dlya uravneniya s vyrozhdeniem na beskonechnosti”, Dif. uravneniya, 3:7 (1967), 1166–1179

[5] Mazya V. G., Prostranstva S. L. Soboleva, Izd. LGU, L., 1985, 415 pp. | MR

[6] Benedek A., Panzone R., “The spaces $L_p$, with mixed norm”, Duke Math. J., 28:3 (1961), 302–324 | DOI | MR

[7] Sharapudinov I. I., “O topologii prostranstva $\mathcal L^{p(t)}([0,1])$”, Mat. zametki, 26:4 (1979), 613–632 | MR | Zbl

[8] Bandaliev R. A., “Ob odnom neravenstve v prostranstve Lebega so smeshannoi normoi i s peremennym pokazatelem summiruemosti”, Mat. zametki, 84:3 (2008), 323–333 | DOI | MR | Zbl

[9] Smirnov V. I., Kurs vysshei matematiki, v. 5, Fizmatgiz, M., 1959, 655 pp. | MR

[10] Kufner A., Persson L.-E., Weighted inequalities of Hardy type, World Scientific Publishing Co, New Jersey–London, 2003 | MR | Zbl

[11] Khardi G. G., Littlvud D. E., Polia G. P., Neravenstva, Izd-vo inostr. lit-ry, M., 1948