Lebesgue and Vilenkin-Lebesgue points and a. e. Convergence of N\"orlund means with respect to Vilenkin systems of integrable functions

TL;DR

This paper investigates the pointwise and norm convergence of Nörlund means of Vilenkin-Fourier series for integrable functions, focusing on Lebesgue and Vilenkin-Lebesgue points, and establishes convergence results in these contexts.

Contribution

It provides new convergence theorems for Nörlund means of Vilenkin-Fourier series at Lebesgue and Vilenkin-Lebesgue points, expanding understanding of their behavior for integrable functions.

Findings

Convergence of Nörlund means at Lebesgue points

Convergence at Vilenkin-Lebesgue points

Norm convergence in Lp spaces

Abstract

In this paper we derive converge of N\"orlund means of Vilenkin-Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilinkin-Lebesgue points. Moreover, we discuss pointwise and norm convergence in $L_p$ norms of such N\"orlund means.