An Integrability Theorem on Unbounded Vilenkin Groups

An analogue of the classical Fomin′s theorem holds in general Vilenkin systems. We prove this using F. Riesz′s general version of the Hausdorff-Young inequality on the cosets of a subgroup of a given Vilenkin group. The class of sequences involved and the class of quasiconvex sequences are incomparable.