Geodesic
On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 616-631

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The closure of the set of smooth compactly supported functions in a weighted Hölder space on $\mathbb R^n$, $n\ge 1$, with a weight controlling the behavior at the point at infinity is described. As an application, a solvability criterion for operator equations generated by de Rham differentials both in these spaces and on the closure of the set of smooth compactly supported functions in them for $n\ge 2$ is obtained.
Keywords: weighted Hölder spaces, de Rham complex. 
@article{MZM_2019_105_4_a11,
     author = {K. V. Sidorova (Gagelgans) and A. A. Shlapunov},
     title = {On the {Closure} of {Smooth} {Compactly} {Supported} {Functions} in {Weighted} {H\"older} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {616--631},
     publisher = {mathdoc},
     volume = {105},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/}
}
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K. V. Sidorova (Gagelgans); A. A. Shlapunov. On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 616-631. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/