Restriction Estimates for space curves with respect to general measures

Abstract

In this paper we consider adjoint restriction estimates for space curves with respect to general measures and obtain optimal estimates when the curves satisfy a finite type condition. The argument here is new in that it doesn't rely on the \emph{offspring curve} method, which has been extensively used in the previous works. Our work was inspired by the recent argument due to Bourgain and Guth which was used to deduce linear restriction estimates from multilinear estimates for hypersurfaces.

24 pages, 1 figure

References in corpus (1)

• The Fourier extension operator on large spheres and related oscillatory integrals

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• Remarks on estimates for the adjoint restriction operator to curves over the sphere
• Averaged decay estimates for Fourier transforms of measures over curves with non vanishing torsion