Fourier restriction estimates for space curves

Abstract

For the Fourier transformation of a Schwartz function f, one can ask for which p, q and subsets S we can meaningfully restrict the Fourier transform. That is, what geometrical property of a set S makes it possible to have the estimate. In this paper, we will cover cases when a set S is a curve with certain non-degeneracy property. The purpose of this paper is to survey historical progress to deal with local restriction estimates for non-degenerate curves. Doing this, we review methods related to the restriction theorem and limitations come from those methods.