A note on the derivative and approximation of almost periodic functions (Q1379846)

There are investigated properties of functions belonging to various classes of almost periodic functions, namely \(S\)-a.p., \(H\)-a.p., \(V\)-a.p., \(L_\alpha\)-a.p. (almost periodic functions in the sense of Stepanov, Hausdorff, variation, \(\text{Lip }\alpha\), respectively), with application of the modulus of non-monotonicity \(\mu_f(\delta)\) of a function \(f\). There are given sufficient conditions under which the derivative \(f'\) of an a.p. function \(f\) is again a.p. in the same sense. Also, almost periodicity and approximation properties of Steklov functions (i.e., integral means of a function \(f\)) are investigated.