On the Fourier dimension of $(d,k)$-sets and Kakeya sets with restricted directions

Jonathan M. Fraser, Terence L. J. Harris, Nicholas G. Kroon

A $(d,k)$-set is a subset of ${\mathbb{R}}^d$ containing a $k$-dimensional unit ball of all possible orientations. Using an approach of D.~Oberlin we prove various Fourier dimension…