Tangential limits and removable sets for weighted Sobolev spaces (Q1409325)

In [Ark. Mat. 37, 291-304 (1999)], \textit{P. Koskela} studied removability of sets for Sobolev spaces \(W^{1,p}\). A set \(E\subset\mathbb R^{n-1}\) is said to be removable for \(W^{1,p}\) if \(W^{1,p}(\mathbb R^n\backslash E)=W^{1,p}(\mathbb R^n)\) as sets; \(n\geq 2\). The author obtains a generalization of Koskela result for the weighted Sobolev space with the weight \(|x_n|^\alpha\), \(-1<\alpha <p-1\). His result runs as follows. A set \(E\) is removable for \(W^{1,p}(\mathbb R^n, |x_n|^\alpha dx)\), \(1<p<n+\alpha \), if \(E\) is \((p-\alpha)\)-porous, the latter notion being introduced in Koskela's paper cited above.