Nikol'skij-type and maximal inequalities for generalized trigonometric polynomials

We consider some Nikol'skij-type inequalities, thus inequalities between different metrics of a function, for almost periodic trigonometric polynomials. Some basic methods of probability theory are applied to prove the existence of the distribution function for an almost periodic function in the sense of Besicovitch. Finally, the Maximal function of Hardy and Littlewood is considered and maximal inequalities on Besicovitch spaces are proved.