In this paper a generalization of some results from Fourier analysis on periodic function spaces to the almost periodic case is given. We consider almost periodic distributions which constitute a subclass of tempered distributions. Under suitable conditions on the spectrum \Lambda \subset \mathbb R^s , a distribution T \in S'(\mathbb R^s) is almost periodic if it can be represented as \sum_{\lambda \in \Lambda} a_{\lambda} e^{i \lambda x} , where the sequence (a_{\lambda})_{\lambda \in \Lambda} is tempered. The main result states that any Fourier multipliers for L^q(\mathbb R^s) of the Michlin-Hörmander type is also a Fourier multiplier for the Besicovich spaces B^q_{ap} (\mathbb R^s, \Lambda) , if it is restricted to the spectrum \Lambda . Finally, we prove that the Sobolev-Besicovich spaces H^{N,q}_{sp} (\mathbb R^s, \Lambda) coincide if N \in \mathbb N .