Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions

TL;DR

This paper investigates the convergence properties of T means of Vilenkin-Fourier series for integrable functions, focusing on Lebesgue and Vilenkin-Lebesgue points, and discusses both pointwise and norm convergence in Lp spaces.

Contribution

It establishes convergence results of T means at Lebesgue and Vilenkin-Lebesgue points for integrable functions, extending understanding of Vilenkin-Fourier series behavior.

Findings

Convergence of T means at Lebesgue points

Convergence at Vilenkin-Lebesgue points

Norm convergence in Lp spaces

Abstract

In this paper we derive converge of $T$ 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 $T$ means.