Restriction conjecture

In harmonic analysis, the restriction conjecture, also known as the Fourier restriction conjecture, is a conjecture about the behaviour of the Fourier transform on curved hypersurfaces. It was first hypothesized by Elias Stein. The conjecture states that two necessary conditions needed to solve a problem known as the restriction problem in that scenario are also sufficient.
The restriction conjecture is closely related to the Kakeya conjecture, Bochner-Riesz conjecture and the local smoothing conjecture.

Statement

The restriction conjecture states that for certain q and n, where represents the L^p norm, or and means that for some constant.
The requirements of q and n set by the conjecture are that and.
The restriction conjecture has been proved for dimension as of 2021.