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Strongly singular Radon transforms on the Heisenberg group and folding singularities

By Norberto Laghi and Neil Lyall


We prove sharp L² regularity results for classes of strongly singular Radon transforms 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

Year: 2007
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