A scale of almost periodic functions spaces

Abstract

This paper contains a construction of a scale of almost periodic functions spaces, extending from the space of functions representable as sums of absolutely convergent series of complex exponentials, up to the space of Besicovitch, the largest for which the Parseval equality holds. Instead of using integral norms, that have been used in constructing almost periodic functions (Stepanov, Weyl, Besicovitch), one uses Minkowski's norms in the linear space of trigonometric polynomials, then completes the last space, endowed with Minkowski's norms with various indices between 1 and 2.