Multidimensional analogues of direct and converse Jackson and Bernshtein theorems and their generalizations
For a bounded domain \(G\) in \(\mathbb R^n\) \((n\geq 2)\) with Lipschitz boundary and a relatively compact, open subset \(D\) of \(G\), the author proves the embeddings \(B^\alpha_{p,q}(G)\subset E^\alpha_{p,q}(G)\subset B^\alpha_{p,q}(D)\), where \(E^\alpha_{p,q}(G)\) is an approximation subspace of \(L_p(G)\) [see \textit{J. Bergh} and \textit{J. Löfstrom}, Interpolation spaces. An Introduction, Springer, Heidelberg (1976; Zbl 0344.46071)], \(1\leq p<\infty\) and \(0<q\leq\infty\).
Jackson, Bernstein and de la Vallée Pousin theorems
scientific article; zbMATH DE number 1531338