A restriction estimate in $\mathbb{R}^3$ using brooms
Abstract
If $f$ is a function supported on the truncated paraboloid in $\mathbb{R}^3$ and $E$ is the corresponding extension operator, then we prove that for all $p> 3+ 3/13$, $\Ef\_{L^p(\mathbb{R}^3)}\leq C \f\_{L^{\infty}}$. The proof combines Wolff's two ends argument with polynomial partitioning techniques. We also observe some geometric structures in wave packets.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.04312
 Bibcode:
 2018arXiv180204312W
 Keywords:

 Mathematics  Classical Analysis and ODEs
 EPrint:
 53 pages, revised version incorporating referees' suggestions