Geometric incidence theorems via Fourier analysis
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- by Alex Iosevich, Hadi Jorati and Izabella Łaba PDF
- Trans. Amer. Math. Soc. 361 (2009), 6595-6611 Request permission
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.References
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Additional Information
- Alex Iosevich
- Affiliation: Department of Mathematics, University of Missouri, 201 MSB, Columbia, Missouri 65211-4100
- MR Author ID: 356191
- 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
- Received by editor(s): February 11, 2007
- Received by editor(s) in revised form: February 4, 2008
- Published electronically: July 24, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 6595-6611
- MSC (2000): Primary 42B35, 28A75
- DOI: https://doi.org/10.1090/S0002-9947-09-04866-1
- MathSciNet review: 2538607