Convergence of 𝑇 means with respect to Vilenkin systems of integrable functions

Abstract

Abstract In this paper, we derive the convergence of 𝑇 means of Vilenkin–Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilenkin–Lebesgue points. Moreover, we discuss the pointwise and norm convergence in L p L_{p} norms of such 𝑇 means.