Radial Fourier restriction to the sphere satisfies a dimension-free endpoint Stein-Tomas bound, general functions lose only d^{1/2}, and best constants tend to zero or infinity according to the Riesz region.
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Dimension-free Fourier restriction inequalities
Radial Fourier restriction to the sphere satisfies a dimension-free endpoint Stein-Tomas bound, general functions lose only d^{1/2}, and best constants tend to zero or infinity according to the Riesz region.