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Transactions of the American Mathematical Society

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Linear and bilinear restriction to certain rotationally symmetric hypersurfaces


Author: Betsy Stovall
Journal: Trans. Amer. Math. Soc. 369 (2017), 4093-4117
MSC (2010): Primary 42-XX
DOI: https://doi.org/10.1090/tran/6783
Published electronically: November 8, 2016
MathSciNet review: 3624403
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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.


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Additional Information

Betsy Stovall
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: stovall@math.wisc.edu

DOI: https://doi.org/10.1090/tran/6783
Received by editor(s): October 23, 2014
Received by editor(s) in revised form: June 8, 2015
Published electronically: November 8, 2016
Article copyright: © Copyright 2016 American Mathematical Society