Vodop’yanov, S. K.; Ukhlov, A. D. Superposition operators in Sobolev spaces. (English. Russian original) Zbl 1033.47020 Russ. Math. 46, No. 10, 9-31 (2002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2002, No. 10, 11-33 (2002). A characterization of the superposition operators \(\varphi^*(f)=f\circ \varphi\) in terms of the generating function \(\varphi\) is given for certain Sobolev spaces. The obtained facts extend the ones discussed in a previous paper by the authors [Sib. Mat. Zh. 39, 776–795 (1998; Zbl 0917.46023)]. Reviewer: Mihai Turinici (Iaşi) Cited in 33 Documents MSC: 47B33 Linear composition operators 30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:superposition operator; Sobolev space; open map; embedding; \(N\)-property Citations:Zbl 0917.46023 PDFBibTeX XMLCite \textit{S. K. Vodop'yanov} and \textit{A. D. Ukhlov}, Russ. Math. 46, No. 10, 11--33 (2002; Zbl 1033.47020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2002, No. 10, 11--33 (2002) Full Text: EuDML