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arXiv · 1006.4319

Existence of Extremals for a Fourier Restriction Inequality

Michael Christ·Shuanglin Shao
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Abstract

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto \widehat{fσ}$ 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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Michael Christ, Shuanglin Shao. 2010-06-22. Existence of Extremals for a Fourier Restriction Inequality. https://arxiv.org/abs/1006.4319

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