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

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 <i><b>L</i></b>_p norms of such T means.