Extensions and imbeddings
Let \(D\) be a bounded domain in \(\mathbb{R}^n\). It is the main aim of this paper to clarify the intimate relationship between the following two properties: (i) Sobolev's embedding \(W^1_p(D)\subset C^\alpha(D)\), \(\alpha=1-{n\over p}\), \(p>n\), (ii) there is a bounded extension operator from the Sobolev space \(W^1_q(D)\) into \(W^1_q(\mathbb{R}^n)\), where \(q>p\). In particular, the dependence of the extension property on \(p\) is discussed.
scientific article; zbMATH DE number 1268051