An endline bilinear cone restriction estimate for mixed norms

TL;DR

This paper establishes a new bilinear Fourier extension estimate for the cone in mixed norm spaces, extending previous results and covering critical line cases.

Contribution

It proves an $L^2 imes L^2 ightarrow L_t^qL_x^p$ estimate for the cone at the critical line, advancing the understanding of Fourier extension problems.

Findings

Extends previous bilinear cone restriction estimates.

Establishes the estimate on the critical line $1/q=(n+1)/2(1-1/p)$.

Provides new tools for analyzing Fourier extension phenomena.

Abstract

We prove an $L^2 \times L^2 \rightarrow L_t^qL_x^p $ bilinear Fourier extension estimate for the cone when $p,q$ are on the critical line $1/q=(\frac{n+1}{2})(1-1/p)$. This extends previous results by Wolff, Tao and Lee-Vargas.