In this paper we continue the study of the Fourier transform on ${\mathbf{R}}^n$, $n\ge 2$, analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of $log\left(N\right)$, where $N$ is the number of equal angles considered in ${\mathbf{R}}^2$. The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of ${\mathbf{R}}^n$, $n\ge 2$, of fixed eccentricity...