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Sets of Salem type and sharpness of the $L^2$-Fourier restriction theorem (1305.5584v2)
Published 24 May 2013 in math.CA
Abstract: We construct Salem sets on the real line with endpoint Fourier decay and near-endpoint regularity properties. This complements a result of \L aba and Pramanik, who obtained near-endpoint Fourier decay and endpoint regularity properties. We then modify the construction to extend a theorem of Hambrook and \L aba to show sharpness of the $L2$-Fourier restriction estimate by Mockenhaupt and Bak-Seeger, including the case where the Hausdorff and Fourier dimension do not coincide.