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Strongly singular Radon transforms on the Heisenberg group and folding singularities
Author(s):
Norberto
Laghi;
Neil
Lyall
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1261-1272.
MSC (2000):
Primary 44A12, 42B20, 43A80
Posted:
December 18, 2007
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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:
10.1090/S0002-9939-07-09236-2
PII:
S 0002-9939(07)09236-2
Keywords:
Strongly singular integrals,
Radon transforms,
folding singularities
Received by editor(s):
November 28, 2006
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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