A theorem of Mockenhaupt (2000) provides a Stein-Tomas type restriction estimate for fractal measures whose Fourier transform decays pointwise at infinity. It has not been known since Mockenhaupt's work whether the range of the exponents in the theorem could be improved, except that an endpoint estimate was proved recently by Bak and Seeger. We prove using arithmetic arguments that this range is indeed optimal for Salem sets on the line. This is joint work with Kyle Hambrook.
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