# A note on the Stein restriction conjecture and the restriction problem on the torus

## TL;DR

This paper investigates the Stein restriction problem on n-tori, establishing necessary and sufficient conditions on Lebesgue indices that are independent of the dimension, contrasting with classical cases like spheres and cones.

## Contribution

It provides a new dimension-independent characterization of Lebesgue indices for the Stein restriction problem on arbitrary n-tori.

## Key findings

- Necessary and sufficient conditions on Lebesgue indices for n-tori
- Conditions are independent of the dimension n
- Contrasts with classical restriction cases like spheres and cones

## Abstract

In this note we discuss the Stein restriction problem on arbitrary $n$-torus, $n\geq 2$. In contrast with the usual cases of the sphere, the parabola and the cone, we provide necessary and sufficient conditions on the Lebesgue indices, by finding conditions which are independent of the dimension $n$.