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Strongly singular Radon transforms on the Heisenberg group and folding singularities


Authors: Norberto Laghi and Neil Lyall
Journal: Proc. Amer. Math. Soc. 136 (2008), 1261-1272
MSC (2000): Primary 44A12, 42B20, 43A80
DOI: https://doi.org/10.1090/S0002-9939-07-09236-2
Published electronically: December 18, 2007
MathSciNet review: 2367100
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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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Additional Information

Norberto Laghi
Affiliation: School of Mathematics, The University of Edinburgh, JCM Building, The King’s Buildings, Edinburgh EH9 3JZ, United Kingdom
Email: N.Laghi@ed.ac.uk

Neil Lyall
Affiliation: Department of Mathematics, The University of Georgia, Boyd Graduate Studies Research Center, Athens, Georgia 30602
Email: lyall@math.uga.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09236-2
Keywords: Strongly singular integrals, Radon transforms, folding singularities
Received by editor(s): November 28, 2006
Published electronically: December 18, 2007
Additional Notes: The first author was partially supported by a HARP grant from the European Commission.
The second author was partially supported by a HARP grant from the European Commission.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2007 American Mathematical Society

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