Geodesic
Modular estimates in orlicz spaces and Hammerstein operator equations
Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 50-59 
P. P. Zabreiko; A. V. Lebedev. Modular estimates in orlicz spaces and Hammerstein operator equations. Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 50-59. http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Certain inequalities between the values of the modular and the norm in the Orlicz spaces are established. These inequalities are applied then to the theory of solvability of nonlinear integral equations of Hammerstein type.

[1] Lebedev A. V., Zabreiko P. P., Modular estimates in Orlicz spaces and Hammerstein operator equations, 10 oct 2005, 11 pp., arXiv: 0510200v1[math.FA]

[2] Krasnosel'skij M. A., Rutitskij Ja. B., Convex functions and Orlicz spaces, Nauka, Moscow, 1958 (in Russian)

[3] Krasnosel'skij M. A., Rutitskij Ja. B., “Orlicz spaces and nonlinear integral equations”, Trudy Moskovskogo matematicheskogo obschestva, 7, 1958, 63–120 (in Russian))

[4] Gel'man I. V., “On a certain nonlinear operator”, Doklady AN SSSR, 120:3 (1958), 454–456 (in Russian) | MR

[5] Rutitskij Ja. B., “On a certain property of the Orlich norm”, Doklady AN SSSR, 138:1 (1961), 56–58 (in Russian) | Zbl

[6] Honda K., “On a Ya. B. Ruticki's theorem concerning a property of the Orlicz norm”, Proc. Japan. Acad., 38:7 (1962), 300–303 | DOI | MR

[7] Zabreiko P. P., Rogozin S. V., “On the solvability and unique solvability of nonlinear singular integral equations in Orlicz spaces”, Doklady Akademii nauk Belarusi, 36:5 (1992), 398–402 (in Russian) | MR | Zbl

[8] Gusejnov A. I., Mukhtarov Kh. Sh., An introduction to the theory of nonlinear integral equations, Nauka, Moscow, 1980 (in Russian)