György Gát, Ushangi Goginava

Almost Everywhere Convergence of $(C,\alpha)$-Means of Quadratical
Partial sums of double Vilenkin-Fourier Series

Abstract:
We prove that the maximal operator of the $\(C,\alpha\)$-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the $(C,\alpha)$-means $t_{n}^{\alpha}f$ of a function $f\in L^{1}$ converge a.e. to $f$ as $n\rightarrow \infty .$

Keywords:
Cesáro means, Vilenkin system, a.e. convergence.

MSC 2000: 42C10