Geodesic
Localization of smooth and smoothing of uniformly continuous mappings
Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 182-195
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The problem of representation of a smooth function as a sum of compactly supported functions of the same smoothness with supports of an arbitrarily small size is solved, as well as the problem of uniform approximation of uniformly continuous (smooth) mappings by mappings having the maximal possible local and uniform smoothness. 
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I. G. Tsar'kov. Localization of smooth and smoothing of uniformly continuous mappings. Trudy Instituta matematiki i mehaniki, Function theory, Tome 11 (2005) no. 2, pp. 182-195. http://geodesic.mathdoc.fr/item/TIMM_2005_11_2_a13/

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