Salem sets and restriction properties of Fourier transforms

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Recent progress on the restriction conjecture (2003, background): “2For surfaces of lower dimension, see [27], [61], [53], [2]; for fractal sets in R, see [54], [67], [53]; for surfaces in finite field geometries, see [55]; for the restriction theory of the prime numbers, see [39].”
Arithmetic Progressions in Sets of Fractional Dimension (2007, background): “The main result in [23] is an L(dx) → L(2)(dμ) bound for the Fourier restriction operator in the range 1 ≤ p < 2(2 − 2α + β)/(4(1 − α) + β).”
Extensions of the Stein-Tomas theorem (2010, methodology): “Our first result concerns an endpoint version of the L2 Stein-Tomas Fourier restriction theorem ([29], [30], [27]), in the following general setup as formulated by Mockenhaupt [21], and also by Mitsis [20].”
Geometric Properties of Fractional Brownian Sheets (2007, unknown): “Mockenhaupt [34]].”
Salem sets with no arithmetic progressions (2015, methodology): “As another example, Mockenhaupt [11] (other than the endpoint) and Bak and Seeger [1] (at the endpoint) showed that measures with Fourier decay that, additionally, have a suitable uniform mass decay, satisfy a restriction theorem analog to the Stein-Tomas restriction theorem for the sphere (in fact,”