On almost everywhere convergence of the generalized Marcienkiwicz means with respect to two dimensional Vilenkin-like systems

Two-dimensional Sunouchi Operator with Respect to Vilenkin-like Systems

In this paper two-dimensional Vilenkin-like systems will be investigated. We prove the Sunouchi operator is bounded from H to L for (2/3 < q ≤ 1). As a consequence, we prove the Sunouchi operator is L bounded for 1 < s < ∞ and of weak type (H, L).

Almost Everywhere Convergence of a Subsequence of the Logarithmic Means of Vilenkin-Fourier Series

Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1,1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...

Convergence of Cesàro Means of Functions with Respect to Unbounded Vilenkin Systems

One of the most celebrated problems in dyadic harmonic analysis is the pointwise convergence of the Fejér (or (C, 1)) means of functions on unbounded Vilenkin groups. The aim of this paper is to give a résumé of the recent developments concerning this matter. Above all, we prove that the maximal operator sup |σMn | is of type (H, L1) on unbounded Vilenkin groups. First, we give a brief introduc...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Almost Everywhere Convergence of Cone-like Restricted Double Fejér Means on Compact Totally Disconnected Groups

In the present paper we prove the a.e. convergence of Fejér means of integrable functions with respect to the two-dimensional representative product systems on a bounded compact totally disconnected group provided that the set of indices is in a cone-like set.