# Mixed norm Strichartz-type estimates for hypersurfaces in three dimensions

## TL;DR

This paper extends Fourier restriction estimates for hypersurfaces in three dimensions to mixed norm cases, providing complete results for adapted cases and partial results for non-adapted cases, especially when the linear height is below two.

## Contribution

It introduces mixed norm Fourier restriction estimates for hypersurfaces, advancing the understanding beyond previous full-range $L^p-L^2$ results.

## Key findings

- Complete resolution for the adapted case.
- Partial results for the non-adapted case.
- Full settlement when linear height is below two.

## Abstract

In their work [IM16] I.A. Ikromov and D. M\"{u}ller proved the full range $L^p-L^2$ Fourier restriction estimates for a very general class of hypersurfaces in $\R^3$ which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed norm case where the coordinates are split in two directions, one tangential and the other normal to the surface at a fixed given point. In particular, we resolve completely the adapted case and partly the non-adapted case. In the non-adapted case the case when the linear height $h_\text{lin}(\phi)$ is below two is settled completely.