Phong, D. H.; Stein, Elias M. Radon transforms and torsion. (English) Zbl 0761.46033 Int. Math. Res. Not. 1991, No. 4, 49-60 (1991). The authors study Radon transforms associated to families of submanifolds with vanishing curvature. It is introduced the notion of nonvanishing generalized torsion for distributions of curves in an \(n\)-dimensional manifold and it is characterized in terms of vector fields. Then the bounds of Radon transforms on \(L^ p-L^ q\) spaces and Sobolev spaces are described. The results are complete for curves in a two-dimensional manifold. In higher dimensions the full general case of distributions with nonvanishing torsion is not considered. Reviewer: L.Simon (Budapest) Cited in 4 ReviewsCited in 39 Documents MSC: 46F12 Integral transforms in distribution spaces 44A12 Radon transform Keywords:Radon transforms; families of submanifolds with vanishing curvature; generalized torsion for distributions of curves in an \(n\)-dimensional manifold; Sobolev spaces; distributions with nonvanishing torsion PDFBibTeX XMLCite \textit{D. H. Phong} and \textit{E. M. Stein}, Int. Math. Res. Not. 1991, No. 4, 49--60 (1991; Zbl 0761.46033) Full Text: DOI