Geodesic
Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 408-417 
O. V. Matveev. Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 408-417. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a8/
@article{MZM_2002_72_3_a8,
     author = {O. V. Matveev},
     title = {Bases in {Sobolev} {Spaces} on {Bounded} {Domains} with {Lipschitzian} {Boundary}},
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     pages = {408--417},
     year = {2002},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the Sobolev space $W_p^k(\Omega )$, where $\Omega$ is a bounded domain in $\mathbb R^n$ with a Lipschitzian boundary, for an arbitrarily given $m\in \mathbb N$, we construct a basis such that the error of approximation of a function $f\in W_p^k(\Omega )$ the $N$th partial sum of its expansion with respect to this basis can be estimated in terms of the modulus of smoothness $\omega _m(D^kf,N^{-1/n})_{L_p(\Omega )}$ of order $m$.

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