RESTRICTION OF FOURIER TRANSFORMS TO CURVES II: SOME CLASSES WITH VANISHING TORSION

Abstract

AbstractWe consider the Fourier restriction operators associated to certain degenerate curves in ℝd for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on the curve. The estimates have certain uniform features, and the affine arclength results cover families of flat curves.