Geodesic
Local approximations on manifolds and weighted estimates
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part VII, Tome 139 (1984), pp. 125-138

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An approach proposed by the author for representing spaces of local functions (s.l.f.) by means of an abstract function with values in the dual space is developed; thanks to this generalization of s.l.f. to the case of a nonuniform net and manifolds are obtained. Moreover, some weighted estimates of approximation by regular s.l.f. are established, and simple proofs are given of theorems of approximation by regular s.l.f. in the spaces of S. L. Sobolev and O. V. Besov. 
@article{ZNSL_1984_139_a8,
     author = {Yu. K. Dem'yanovich},
     title = {Local approximations on manifolds and weighted estimates},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--138},
     publisher = {mathdoc},
     volume = {139},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_139_a8/}
}
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Yu. K. Dem'yanovich. Local approximations on manifolds and weighted estimates. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part VII, Tome 139 (1984), pp. 125-138. http://geodesic.mathdoc.fr/item/ZNSL_1984_139_a8/