Oscillatory Integrals and Fourier Transforms of Surface Carried Measures
نویسندگان
چکیده
We suppose that S is a smooth hypersurface in Rn+1 with Gaussian curvature re and surface measure dS, it) is a compactly supported cut-off function, and we let pa be the surface measure with dßa = u>Ka dS. In this paper we consider the case where S is the graph of a suitably convex function, homogeneous of degree d, and estimate the Fourier transform ßa. We also show that if S is convex, with no tangent lines of infinite order, then /*(*(£) decays as |í|_n''2 provided a > [(n + 3)/2]. The techniques involved are the estimation of oscillatory integrals; we give applications involving maximal functions.
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