$\Lambda$-summability and multiplicators of Hölder classes of Fourier series with respect to character systems

Let $G$ be a Vilenkin group of bounded type. We obtain nessesary and sufficient conditions of uniform $\Lambda$-summability for all Fourier series of $f\in C(G)$ and one of $\Lambda$-summability in $L^1(G)$ for all Fourier series of $f\in L^1(G)$. Also we extend some T. Quek and L. Yap results to the case of general modulus of continuity.