Geodesic
Limit Investigation at Infinity of the Sobolev--Wiener Function Classes in Tube Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 327-335.

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In terms of the Sobolev–Wiener function spaces, the conditions are established under which the functions oscillate with respect to a chosen variable and stabilize to zero. 
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S. V. Uspenskii; E. N. Vasil'eva. Limit Investigation at Infinity of the Sobolev--Wiener Function Classes in Tube Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 327-335. http://geodesic.mathdoc.fr/item/TM_2001_232_a26/

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