Strongly singular Radon transforms on the Heisenberg group and folding singularities

Laghi, Norberto; Lyall, Neil

doi:10.1090/S0002-9939-07-09236-2

Strongly singular Radon transforms on the Heisenberg group and folding singularities
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by Norberto Laghi and Neil Lyall

Proc. Amer. Math. Soc. 136 (2008), 1261-1272

DOI: https://doi.org/10.1090/S0002-9939-07-09236-2

Published electronically: December 18, 2007

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Abstract:

We prove sharp $L^2$ 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.

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