Vodop’yanov, S. K. Mappings of homogeneous groups and imbeddings of functional spaces. (English. Russian original) Zbl 0731.46019 Sib. Math. J. 30, No. 5, 685-698 (1989); translation from Sib. Mat. Zh. 30, No. 5(177), 25-41 (1989). The author investigates the metric and analytic properties of a mapping \(\phi\) defined by an isomorphism \(\phi^*: F\to F'\), \(\phi^*(f)=f\circ \phi\), \(f\in F\) where F and \(F'\) are functional spaces on homogeneous groups. The Sobolev spaces and the Nikolskii spaces are considered as the model examples of F and \(F'\). Reviewer: V.V.Kovrizhkin (Omsk) Cited in 16 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 43A70 Analysis on specific locally compact and other abelian groups Keywords:functional spaces on homogeneous groups; Sobolev spaces; Nikolskii spaces PDFBibTeX XMLCite \textit{S. K. Vodop'yanov}, Sib. Math. J. 30, No. 5, 685--698 (1989; Zbl 0731.46019); translation from Sib. Mat. 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