2019 Fiscal Year Annual Research Report

New developments on the restriction conjecture for the Fourier transform using multilinear analysis

Research Project

Project/Area Number	18F18020
Research Institution	Saitama University
Principal Investigator	BEZ NEAL 埼玉大学, 理工学研究科, 准教授 (30729843)
Co-Investigator(Kenkyū-buntansha)	CUNANAN JAYSON MESITAS 埼玉大学, 理工学研究科, 外国人特別研究員
Project Period (FY)	2018-04-25 – 2020-03-31
Keywords	Kinetic transport / Velocity average / Strichartz estimate / Wave equation
Outline of Annual Research Achievements	Based on techniques arising in the restriction theory of the Fourier transform, several new results were obtained concerning the kinetic transport equation and the wave equation. For the kinetic transport equation, in the case where the velocities belong to the sphere and radially symmetric square-integrable initial data, sharp results were obtained for mixed-norm estimates on velocity averages in the framework of hyperbolic Sobolev spaces. In a different direction, the Keel-Tao approach was used to obtain new inhomogeneous Strichartz estimates of weak type for the wave equation where the so-called acceptability condition fails.
Research Progress Status	令和元年度が最終年度であるため、記入しない。
Strategy for Future Research Activity	令和元年度が最終年度であるため、記入しない。