Geodesic
Qualitative Properties of Functions that Belong to Generalized Sobolev Spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2003_243_a23,
     author = {S. V. Uspenskii and E. N. Vasil'eva},
     title = {Qualitative {Properties} of {Functions} that {Belong} to {Generalized} {Sobolev} {Spaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {346--351},
     publisher = {mathdoc},
     volume = {243},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_243_a23/}
}
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S. V. Uspenskii; E. N. Vasil'eva. Qualitative Properties of Functions that Belong to Generalized Sobolev Spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 346-351. http://geodesic.mathdoc.fr/item/TM_2003_243_a23/