Fourier restriction and well-approximable numbers
Abstract
We use a deterministic construction to prove the optimality of the exponent in the Mockenhaupt-Mitsis-Bak-Seeger Fourier restriction theorem for dimension d=1 and parameter range 0 < a,b ≤ d and b≤ 2a. Previous constructions by Hambrook and aba HL2013 and Chen chen required randomness and only covered the range 0 < b ≤ a ≤ d=1. We also resolve a question of Seeger seeger-private about the Fourier restriction inequality on the sets of well-approximable numbers.
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