Almost everywhere convergence of subsequences of Walsh-Nörlund means

Abstract

Let $\{q_k:k\in \mathbb{N}\}$ be a non-increasing and convex sequence of non-negative numbers such that $q_0>0$. Our main result is to prove almost everywhere convergence \[ t_{a_{n}}(f)\to f \] of $f\in L_1(G)$ as $n\to \infty$, using several $\{a_n:n\in \mathbb{P}\}$ subsequences of positive integers for Nörlund means (defined by sequence $q$) on the Walsh-Paley system with weaker conditions than it was known before.