For convex analytic finite-type hypersurfaces, the square-root curvature damped Fourier transform decays at the optimal rate |ξ|^{-d/2} for d=2,3, and with a logarithmic loss for d=4.
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Damping oscillatory Integrals of convex analytic functions
For convex analytic finite-type hypersurfaces, the square-root curvature damped Fourier transform decays at the optimal rate |ξ|^{-d/2} for d=2,3, and with a logarithmic loss for d=4.