Pre-dual of Fofana's spaces

It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduced by I.~Fofana on the basis of Wiener amalgam spaces. Those spaces have a specific dilation behaviour similar to the spaces $L^\alpha(\mathbb R^d)$. The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).