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

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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.