Existence of Extremals for a Fourier Restriction Inequality

By Michael Christ, Shuanglin Shao. 2010

91 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8aa862d58d16d4aa9924cd796322e8c8b4306803

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In Applied Mathematics

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Citations in the corpus

Maximizers for the Stein–Tomas Inequality (2016, unknown): “These questions were recently considered in fundamental papers by Christ and Shao, where the existence of a maximizer for N = 3 [12] and N = 2 [29] was shown, as well as a precompactness result for maximizing sequences for N = 3 [13].”
Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality (2013, methodology): “3 was proved in [1], our proof here is much shorter and simpler.”
On the existence of maximizers for a family of restriction theorems (2010, background): “In [2], the existence of maximizers for the restriction on the sphere S2 with respect to p = 4 is proved (which turns out to be the end-point value for the restriction on S2).”