Cesaro means of negative order of the quadratic partial sums of double Vilenkin-Fourier series

Abstract

In \cite{TePe} has been proved some inequalities related to the rate of $% L^{p} $ approximation by Ces\`{a}ro means of the quadratic partial sums of double Vilenkin-Fourier series of functions from $L^{p}$. These inequalities
imply sufficient conditions which provide convergence in the norm of Ces\`{a}% ro means of the quadratic partial sums of double Vilenkin-Fourier series in terms of modulus of continuity. In this paper there is proved that these results are sharp in a certain sense.