Some remarks on extension theorems for weighted Sobolev spaces (Q1320964)

Let \(\Omega\) be a Lipschitz domain in \(\mathbb{R}^ n\), then it is well known that there exists a linear and bounded extension operator for the Sobolev spaces \(W^ k_ p(\Omega)\) in \(W^ k_ p(\mathbb{R}^ n)\), \(k\in\mathbb{N}\), \(1\leq p\leq\infty\). This assertion holds also for the more general \((\varepsilon,\delta)\)-domains introduced by P. Jones. The paper deals with corresponding assertions for weighted Sobolev spaces \(W^ k_{p,w(x)}(\Omega)\), where the admitted weights are even more general than the Muckenhoupt classes \(A_ p\).