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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Geometric incidence theorems via Fourier analysis


Authors: Alex Iosevich, Hadi Jorati and Izabella Łaba
Journal: Trans. Amer. Math. Soc. 361 (2009), 6595-6611
MSC (2000): Primary 42B35, 28A75
Published electronically: July 24, 2009
MathSciNet review: 2538607
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Abstract: We show that every non-trivial Sobolev bound for generalized Radon transforms which average functions over families of curves and surfaces yields an incidence theorem for suitably regular discrete sets of points and curves or surfaces in Euclidean space. This mechanism allows us to deduce geometric results not readily accessible by combinatorial methods.


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Additional Information

Alex Iosevich
Affiliation: Department of Mathematics, University of Missouri, 201 MSB, Columbia, Missouri 65211-4100

Hadi Jorati
Affiliation: Department of Mathematics, Princeton University, Washington Road, Fine Hall, Princeton, New Jersey 08544

Izabella Łaba
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04866-1
PII: S 0002-9947(09)04866-1
Received by editor(s): February 11, 2007
Received by editor(s) in revised form: February 4, 2008
Published electronically: July 24, 2009
Article copyright: © Copyright 2009 American Mathematical Society