The Mockenhaupt-Mitsis-Bak-Seeger restriction exponent is optimal for all d and all 0<a,b<d, via deterministic Salem set constructions.
Explicit Salem sets in $\mathbb{R}^n$
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We construct the first explicit (i.e., non-random) examples of Salem sets in $\mathbb{R}^n$ of arbitrary prescribed Hausdorff dimension. This completely resolves a problem proposed by Kahane more than 60 years ago. The construction is based on a form of Diophantine approximation in number fields.
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Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem in all dimensions
The Mockenhaupt-Mitsis-Bak-Seeger restriction exponent is optimal for all d and all 0<a,b<d, via deterministic Salem set constructions.