On the restriction theorem for the paraboloid in ${\mathbb R}^4$
Volume 156 / 2019
Colloquium Mathematicum 156 (2019), 301-311
MSC: Primary 42B15; Secondary 42B20.
DOI: 10.4064/cm7393-9-2018
Published online: 14 February 2019
Abstract
We prove that the recent breaking (Zahl, 2018) of the $3/2$ barrier in Wolff’s estimate on the Kakeya maximal operator in ${\mathbb R}^4$ leads to improving the $14/5$ threshold for the restriction problem for the paraboloid in ${\mathbb R}^4$. One of the ingredients is a slight refinement of a certain trilinear estimate (Guth, 2016). The proofs are deliberately presented in a non-technical and concise format, so as to make the arguments more readable and focus attention on the key tools.
