Strongly singular Radon transforms on the Heisenberg group and folding singularities

Details Strongly singular Radon transforms on the Heisenberg group and folding singularities Strongly singular Radon transforms on the Heisenberg group and folding singularities

2006-10-30

arxiv.org/abs/math/0610908v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

We prove sharp $L^2$ regularity results for classes of strongly singular Radon transfoms on the Heisenberg group by means of oscillatory integrals. We show that the problem in question can be effectively treated by establishing uniform estimates for certain oscillatory integrals whose canonical relations project with two-sided fold singularities; this new approach also allows us to treat operators which are not necessarily translation invariant.

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