Existence of Extremals for a Fourier Restriction Inequality

Details Existence of Extremals for a Fourier Restriction Inequality Existence of Extremals for a Fourier Restriction Inequality

2010-06-22

arxiv.org/abs/1006.4319v1

Mathematics

Classical Analysis and ODEs

52 pages

Scientific paper

The adjoint Fourier restriction inequality of Tomas and Stein states that the
mapping $f\mapsto \widehat{f\sigma}$ is bounded from $\lt(S^2)$ to
$L^4(\reals^3)$. We prove that there exist functions which extremize this
inequality, and that any extremizing sequence of nonnegative functions has a
subsequence which converges to an extremizer.

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