Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary

O. V. Matveev

Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 408-417

Résumé

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 $m$.