Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

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.