Fourier transform, L² restriction theorem, and scaling

2001/04/08 by Alex Iosevich
Mathematics · #math.CA

paper · pdf

published as Bolletino U.M.I., Volume 8 (1999), pp. 383-387

arxiv created 2001/04/08 · arxiv updated 2009/11/30

Abstract

We show, using a Knapp-type homogeneity argument, that the (L^p, L²) restriction theorem implies a growth condition on the hypersurface in question. We further use this result to show that the optimal (L^p, L²) restriction theorem implies the sharp isotropic decay rate for the Fourier transform of the Lebesgue measure carried by compact convex finite hypersurfaces.

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