On the Coefficients of Multiple Series with Respect to Vilenkin System

We give a sufficient condition for coefficients of double series Σ Σn,m an,m χn,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.

Uniqueness of Almost Everywhere Convergent Vilenkin Series

D. J. Grubb [3] has shown that uniqueness holds, under a mild growth condition, for Vilenkin series which converge almost everywhere to zero. We show that, under even less restrictive growth conditions, one can replace the limit function 0 by an arbitrary f ∈ Lq, when q > 1.