Almost everywhere convergence of T means with respect to the Vilenkin system of integrable functions

Abstract

UDC 517.5 We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of  T means with respect to the Vilenkin system generated by monotone coefficients.  We also apply these results to prove that  these T means are  almost everywhere convergent. As applications, we present both some well-known and new results.