#### Vol. 5, No. 2, 2012

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Existence of extremals for a Fourier restriction inequality

### Michael Christ and Shuanglin Shao

Vol. 5 (2012), No. 2, 261–312
##### Abstract

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