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Radon transforms and torsion. (English) Zbl 0761.46033

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)

MSC:

46F12 Integral transforms in distribution spaces
44A12 Radon transform
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