On the extremizers of an adjoint Fourier restriction inequality

By Michael Christ, Shuanglin Shao. 2010

61 citations recorded by the source corpus.

The adjoint Fourier restriction inequality for the sphere $S^2$ states that if $f\in\lt(S^2,\sigma)$ then $\widehat{f\sigma}\in L^4(\reals^3)$. We prove that all critical points $f$ of the functional $\norm{\widehat{f\sigma}}_{L^4}/\norm{f}_{\lt}$ are smooth; that any complex-valued extremizer for the inequality is a nonnegative extremizer multiplied by the character $e^{ix\cdot\xi}$ for some $\xi$; and that complex-valued extremizing sequences for the inequality are precompact modulo multiplication by characters.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e9ce036f9f7fe244ea64e3b3473b9100389fe0a6

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Existence of Extremals for a Fourier Restriction Inequality (2010, methodology): “Equation (1-2) will be used in a forthcoming paper [Christ and Shao 2012] to prove that all critical points are infinitely differentiable.”
Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality (2013, background): “[2] Michael Christ and Shuanglin Shao.”