Lanza de Cristoforis, Massimo A note on composition operators in Sobolev spaces and an extension of the chain rule. (English) Zbl 0723.47027 Rend. Accad. Naz. Sci. Detta XL, V. Ser. Mem. Mat. 14, No. 1, 341-360 (1990). Summary: We study the operator T defined by T[f,g](x)\(\equiv f(g(x))\) from special subsets of \(W^{m,p}(\Omega_ 1)\times (W^{m,q}(\Omega))^ n\) to \(W^{m,r}(\Omega)\). Conditions are found in order to ensure continuity and boundedness of T on bounded sets. Cited in 1 Document MSC: 47B38 Linear operators on function spaces (general) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:composition operators in Sobolev spaces; continuity; boundedness PDFBibTeX XMLCite \textit{M. Lanza de Cristoforis}, Rend. Accad. Naz. Sci. Detta XL, V. Ser., Mem. Mat. 14, No. 1, 341--360 (1990; Zbl 0723.47027)