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

Published electronically:
December 18, 2007

MathSciNet review:
2367100

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Abstract: We prove sharp 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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Ph.D. Thesis, University of Wisconsin-Madison, 1985.

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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:
http://dx.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