On convergence of Fourier–Vilenkin series in $L^p[0,1)$, $0<p\le1$

In this paper we study convergence a.e. and $L^p$-convergence ($0<p\le1$) of Fourier–Vilenkin series under some tauberian conditions on Fourier coefficients of a function. In the case of Fourier–Walsh series these results are obtained by F. Moricz.