Qualitative Properties of Functions that Belong to Generalized Sobolev Spaces
Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 346-351.

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For functions defined in a cylindrical domain, oscillation conditions with respect to a distinguished variable are established and estimates for the rate of stabilization to zero are derived. The oscillation conditions are expressed in terms of special Banach spaces introduced by the authors.
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S. V. Uspenskii; E. N. Vasil'eva. Qualitative Properties of Functions that Belong to Generalized Sobolev Spaces. Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 346-351. http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a23/

[1] Uspenskii S. V., “O teoremakh vlozheniya dlya vesovykh klassov”, Tr. MIAN, 60, 1961, 282–303 | MR | Zbl

[2] Sobolev S. L., “Plotnost finitnykh funktsii v prostranstve $L_p^m$”, Sib. mat. zhurn., 4:3 (1963), 673–682 | MR | Zbl

[3] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975, 480 pp. | MR | Zbl

[4] Sedov V. N., “O funktsiyakh, obraschayuschikhsya v beskonechnosti v polinom”, Teoremy vlozheniya i ikh prilozheniya, 1970, 204–212, Nauka, M. | MR

[5] Kudryavtsev L. D., “O stabilizatsii funktsii v beskonechnosti k resheniyam differentsialnykh uravnenii”, Dif. uravneniya, 11:2 (1975), 332–357

[6] Kudryavtsev L. D., “Polinomialnaya stabilizatsiya i ee prilozheniya v teorii obyknovennykh differentsialnykh uravnenii”, Dif. uravneniya, 29:9 (1993), 1486–1503 | MR | Zbl

[7] Uspenskii S. V., Chistyakov B. N., “O vykhode na polinom pri stremlenii $|x|\to\infty$ reshenii odnogo klassa psevdodifferentsialnykh uravnenii”, Sib. mat. zhurn., 16:5 (1975), 1053–1070 | MR | Zbl

[8] Uspenskii S. V., Vasileva E. N., “Issledovanie na beskonechnosti klassov funktsii Soboleva–Vinera v tsilindricheskikh oblastyakh”, Tr. MIAN, 232, 2001, 327–335 | MR | Zbl