Linear and bilinear restriction to certain rotationally symmetric hypersurfaces
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Abstract:
Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we obtain uniform—depending only on the dimension and polynomial degree—estimates for restriction with affine surface measure, slightly beyond the bilinear range. The main step in the proof of our linear result is an (unconditional) bilinear adjoint restriction estimate for pieces at different scales.References
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Additional Information
- Betsy Stovall
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 881244
- Email: stovall@math.wisc.edu
- Received by editor(s): October 23, 2014
- Received by editor(s) in revised form: June 8, 2015
- Published electronically: November 8, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4093-4117
- MSC (2010): Primary 42-XX
- DOI: https://doi.org/10.1090/tran/6783
- MathSciNet review: 3624403