Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff–Young inequality

We establish the existence of Salem sets in the ring of integers of any local field and study the Fourier restriction phenomenon on such sets. Optimal extension of the Hausdorff–Young inequality, initially attained for the torus by G. Mockenhaupt and W. Ricker, is also established in the local field setting. © 2010 Elsevier Inc. All rights reserved