Functions of translation
type were introduced by H. Reiter and studied by the author in some detail. In this
paper we introduce a class of Banach spaces of functions on a locally compact
group, including the spaces ℳp(G) of Liu-van Rooij-Wang. Necessary and
sufficient conditions are given under which these spaces can be characterized by
functions of translation type. As application it is shown that a sub-class of these
spaces, including Wiener’s algebra, satisfies a certain minimality property.
Furthermore, we obtain a generalization of a theorem on Fourier transforms, due to
Edwards-Hewitt-Ritter, in a very simple manner, whereas the original proof took
several pages.
