Weakly Almost Periodic and Uniformly continuous functionals on the Orlicz Figa Talamanca Herz algebras

Abstract

In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Fig\`a-Talamanca Herz algebras associated to a locally compact group. We show that a unique invariant mean exists on the space of weakly almost periodic functionals. We also characterise discrete groups in terms of the inclusion of the space of uniformly continuous functions inside the space of weakly almost periodic functionals.