Banach convolution algebras of functions II

LetG be a noncompact, locally compact group. By means of generalized dyadic decompositions ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofL^p-spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.With 1 Figure