Farkaş, Walter A Calderón-Zygmund extension theorem for abstract Sobolev spaces. (English) Zbl 0855.46023 Stud. Cercet. Mat. 47, No. 5-6, 379-395 (1995). Summary: It is shown that if the Boyd indices of the rearrangement invariant Banach function space \(L_\rho (\mathbb{R}^n)\) are strictly between 0 and 1, \(\rho\) is an absolutely continuous function norm, \(\Omega\) is a domain from \(\mathbb{R}^n\) satisfying the restricted cone condition, denoting by \(\omega\) the restriction of \(\rho\) to \(\Omega\), there exists an extension operator for the abstract Sobolev space \(W^m L_\omega (\Omega)\). This is a generalization to abstract Sobolev spaces of a result obtained by de Souza for Orlicz-Sobolev spaces. Cited in 3 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:Calderon-Zygmund extension; Boyd indices; rearrangement invariant Banach function space; absolutely continuous function norm; abstract Sobolev space; Orlicz-Sobolev spaces PDFBibTeX XMLCite \textit{W. Farkaş}, Stud. Cercet. Mat. 47, No. 5--6, 379--395 (1995; Zbl 0855.46023)