|Date||Sep 25, 2023|
In this talk, we review the paper entitled "A sharp Mizohata-Takeuchi type estimate for the cone in $\mathbb R^3$" by A. Ortiz. We begin with Mizohata-Takeuch conjecture for the parabola. Then we study the main estimate and related estimates such as weighted Fourier extension estimates, or fractal local smoothing estimates for the wave equation. The key ingredients in proof of the main estimate are pointwise decay for the Fourier transform of the surface measure on the cone and sharp $L^3$ estimates for Wolff's maximal function.