Fourier transform, $L^2$ restriction theorem, and scaling

Details Fourier transform, $L^2$ restriction theorem, and scaling Fourier transform, $L^2$ restriction theorem, and scaling

2001-04-08

arxiv.org/abs/math/0104097v1

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

Mathematics

Classical Analysis and ODEs

Scientific paper

We show, using a Knapp-type homogeneity argument, that the $(L^p, L^2)$
restriction theorem implies a growth condition on the hypersurface in question.
We further use this result to show that the optimal $(L^p, L^2)$ 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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