RESTRICTION ESTIMATES FOR ARBITRARY CONVEX CURVES IN R2

Abstract

We study the restriction estimate of Fourier transform to arbitrary convex curves in R2 with no regularity assumption. Assuming that the convex curve has the lower bound of curvatures, we extend the restriction results from smooth convex curves to arbitrary convex curves. Our work has been motivated by the lecture notes of Terence Tao. The bilinear approach and geometric observations play an important role.

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