On a special Schauder basis for the Sobolev spaces \(W_ 0^{1,p}(\Omega)\)
The author proves the existence of a Schauder basis of \(W_0^{1,p} (\Omega)\) (where \(\Omega\) is a general smooth subdomain of \(\mathbb{R}^n\)) with a property that is weaker than that of having elements that are mutually orthogonal in \(L^2 (\Omega)\) but that can usefully be substituted for it in some contexts. To wit, let \(\{w^i \}_{i\geq 1}\) be a Schauder basis of \(W_0^{1,p} (\Omega)\) and \(V_n\) the closure in \(L^2\) of the subspace of \(W_0^{1,p}\) spanned by the subsequence \(\{w^i \}_{i >n}\). The author shows the existence of a basis with the property that \(\forall n\) \(V_n\cap \text{Span} \{w^1, \dots, w^n\}=0\).
scientific article; zbMATH DE number 766566