Linear and bilinear restriction to certain rotationally symmetric hypersurfaces
Classical Analysis and ODEs
2017-10-24 v1
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.
Keywords
Cite
@article{arxiv.1710.07683,
title = {Linear and bilinear restriction to certain rotationally symmetric hypersurfaces},
author = {Betsy Stovall},
journal= {arXiv preprint arXiv:1710.07683},
year = {2017}
}
Comments
This is a preprint version of a published article. The final version appears in Trans. Amer. Math. Soc. 369 (2017), no. 6, 4093--4117